The proper method will depend on your build. Important factors being:
>are you a glass cannon or are you tanky?
>are you ranged (guns/psi) or melee? and do you have throwing?
>do you have sure step, wear metal boots, or use the stilts?
>if its the 2nd invasion or later, do you have a jet?
>and can you activate the turret and/or naga?
NATIVES
Kriegsfars and spaeters have no armor (a bit of DR, but no DT), skaerders have a bit but not much. Frags and JHP rounds are very effective against them, though I talk about explosives later on. Spaeters like to cast pseudo-spatial projection on themselves (the mirror images spell), which makes individual attacks usually miss; nets and grenades still work just fine, as well as other attacks that can't miss like neural overload or plasma beam. Kriegsfars aren't all the same, defensively. Hammer ones are tough with thick skull, but lower dodge/evasion. Sword ones have the highest dodge/evasion and move points. The spear ones do have spear throw, but very rarely use it for some reason; regardless, watch out for their increased reach. All the melee natives have taste for blood, so if you're bleeding you better use some coagulant shots. If you rely on heavy armor, watch out, they have many ways to lower your armor and/or increase their damage against you. Natives love to throw nets; escape artist is very useful, as is expecting to be netted regardless. They use crippling strike a lot, so be careful if your equipment has strength requirements (maybe switch to something that doesn't, especially if your str isn't 6 points higher than the requirement).
XBOW NATIVES
The xbow natives are generally the biggest threat during invasions (except the rare snake-arm skaerders; they will usually 1hko you from a distance); they have aimed shot and poisoned special bolts. Buff your evasion as much as you can if you are a light character, have plenty of antidotes (and irongut, jumping bean, and aegis, if you can make them). A low/low efficient shield is best. If you can't effectively wear full tungsten armor (regen vest is best for that), then go for high DR (infused sea wyrm is a great option in general), a sturdy reinforced nanocomposite tacvest or otherwise focus on getting higher evasion. The laylow drink from the drag'n'drop is an ideal food for invasions, imo, but if you're a tungsten tank you'll want a crab sandwich (with that and an energy shield, your DT might very well fully block xbow bolts). The tchortist bioscrubber + irongut will make you completely immune to all poison damage (all bio damage period).
THE BEACH
The beach is separated into the upper beach and the lower beach; everywhere from the slopes to the waters edge is the lower beach. Aegis soldiers will NEVER move down the slopes, except when the battle is over. I prepare the lower beach beforehand with caltrops and traps. The auto-turret is a great ally, but don't stand in front of it unless you are bullet-immune. Aegis like to waste grenades at bad times, waste special attacks on almost-dead enemies, wake up incapped enemies with puny attacks, etc. The soldiers on the east side are xbow pincushions. Just keep yahota alive and any other snipers you might have.
EDIT: somehow forgot to mention that there are two stands of rock on the beach that block line of sight, though not much; you can use these for cover if you are running around down there
CALTROPS
Almost every build will want to put down caltrops and bear traps. I will attach images below showing where to put them. If you are immune to caltrops, theres no reason not to coat the entire lower beach. If you are NOT immune to caltrops, and are either very very hard to hit, very very tanky, or both, you might not put down any caltrops so you can camp the boats. Outside of that one exception, you're going to want them. Which caltrops to use (and where) depends on your biology (and mechanics) skill; you can find or buy burrower/cave ear/crawler caltrops, but not in high number or reliably. Regular caltrops are better than nothing, but here's the breakdown:
>caltrops
>burrower (extra damage)
>cave ear (lower crossbow/snake arm accuracy, extra damage from other poisons and toxic gas)
>crawler (some bio damage, 2 turn stun afterwards)
>blinding (extra damage and ranged accuracy; stacks with both burrower and cave ear)
There are several ways to go with this. Cave ear will lower xbow accuracy and make toxic gas and other poisons more effective, so its best to place this down right where they exit the boats. After that should come crawler to give them a stun as they approach the slopes. If theres any space left, blinding poison is the best choice for it. You can also switch crawler out for blinding poison to max the perception drain and deal way more poison damage, and use crawler bear traps to inflict stun (effectively holding them in place for four turns, or 2 + 2 turns of daze if they have thick skull). Most people don't invest in traps however and are limited to regular bear traps or burrower. Most of the time when I do invasions, I just put down crawler catrops where they get off the boat, because I usually like to be able to go down on the beach myself later and help mop up the xbow natives at the end of the fight.
BEAR TRAPS
Bear traps are great, whether you have traps skill or not. If you do, its nice to get the natives stuck in certain positions to block the movements of others and to lower their evasion to 0. If you don't, the natives will probably spot your traps before walking into them, which is still useful because it will deter them from certain paths, corraling them together where you want them (if you dont coat the entire beach in caltrops, they can also serve this purpose). You can do poisoned bear traps if you like; mixing and matching them with the various caltrops can lead to some very nice combos, but I find it to be overkill for most builds. Leper bear traps are probably the best option in general, if you're going to go with poisons, but as said earlier crawler bear traps also serve a purpose. You might think its a good idea to use chem traps instead of bear traps, but given all the explosions that are going to be happening on the beach (depending on your build, but aegis like to throw nades and plant mines themselves), I don't suggest them. Quick-tinkering is a great addition; it lets you pull off some more advanced tactics, like sealing yourself behind traps or plugging a gap in a chokepoint at the last second.
MINES
Mines come in three varieties: frags, HEs, and plasma. Frags deal the most damage to natives, but the damage falls off with distance from the center of the explosion. HEs deal the same damage throughout their area. Plasma deals even more damage (and less resisted damage) than HEs, but have a smaller area and are more expensive and require high electronics skill (or high traps skill to recover the ones you find in-game). One mine will set off another mine, which can chain the whole beach in one giant explosion, so I like to place them so they don't set each other off, though sometimes I will put down a few where the natives exit the boats to catch a whole group. You can have more separate explosions with plasma mines due to their smaller area, so they might be the objective best choice.
GRENADES
Grenade explosions work the same as mines. Frags are the best against lone natives or tight clusters, especially the weaker ones like xbowmen and spaeters, but the best grenade to use during invasions is incendiaries. For one, they deal some damage, they can fear the natives, causing them to forget what they were doing and run away (through caltrops and into traps), they light up the beach providing higher accuracy for your allies, and they provide a lasting AoE that natives will generally steer around, which further helps corral the natives where you want them. Napalm molotovs are the best, since they deal more damage and, more importantly, last longer. You can have the entire beach on fire if you use napalm mollies with grenadier and LTI. Beach invasions are the best time to make use of napalm. In addition to molotovs, I also throw a flare every turn to light up various spots of the beach to increase accuracy, trigger ambush (some aegis soldiers have ambush; they might all have it for all I know), and make it harder for the rare stealthed native.
TOXIC GAS
Toxic gas grenades are fantastic during invasions. The toxic gas can inhabit the same space as caltrops, traps, and fire (as opposed to cryogas), deals bio damage, and increases all damage taken from all sources. I like to plop one down just outside the first boat where the natives have to walk through, and if you have grenadier and/or LTI, you have time to throw down a second and possibly even a third at the second and third boat respectively, then switch to a different utility (though you can keep them equipped and throw down more during the fight). You'll need to go down onto the lower beach to throw toxic gas at the boats (unless you're on a jet); this might be an issue if you are using caltrops and traps.
UTILITIES
My usual utilities loadout during an invasion is: nets, molotovs, stingballs/flashbangs (after throwing toxic gas before combat starts). Stingballs don't work on enemies with thick skull like skaerders or hammer kriegsfars (though they can daze them), they have a smaller AoE, and the stun only lasts 1 turn, but it allows you to hit them multiple times without them waking up; these are best if you're about to lay down some heavy damage on a group of kriegsfars/spaeters. Stingballs can be resisted with armor, but thankfully only skaerders have any. Flashbangs work on all natives, though the spaeters have a good chance to resist, and they last a few turns as long as nothing damages the incapacitated native(s); I like to knock clusters of xbowmen out of the fight with these if I have the chance. If I have a fourth utility slot I prefer tasers. I use nets on skaerders since they are easier to hit, much tankier, less numerous, and more dangerous than other natives. If you are a throwing-knives build; obviously you'll want to make room for knives.
POSITIONING
There are basically five places to park yourself during an invasion, depending on your build. If you're a tank, I like to park myself in front of the plasma turret and put bear traps around myself (if you have the time to seal yourself off before the fight starts, do so). If you're squishy and/or long-ranged, I like to stand near the auto-turret, between it and the plasma turret (ranged characters might also move over to the other side, near the plasma turret, but behind the aegis soldiers). If you don't want to actually fight and have stealth, the far northeast corner of the beach is the best hiding spot. If you are on a jetski, the southwest native boat has a spot behind it where nobody has line-of-sight to you. There is a spot near the ruined tower in the middle that will block line-of-sight from almost the entire lower beach at once. See the positioning image below.
If you want to camp the boats, each native boat has a spot with no line-of-sight to other boats.
PLASMA TURRET
If you can wake up the plasma turret and the naga, do so. They are immensely helpful. The turret has xbow range, no penalty from darkness, immense accuracy, deals a lot of damage, and fires twice per turn. It is basically one or two dead natives every turn; I dont think ive ever seen even a skaerder survive two hits. It also is pretty tanky and takes little damage from xbow shots; this takes some heat off of you and aegis.
NAGA
The naga patrols the near side of the lower beach, has good detection so can usually spot your traps and walk around them (and is immune to bear traps anyway, though it will trigger them if its path is blocked, so make sure to leave it a path), won't take damage from your lasting molotov flames, is immune to caltrops, has excellent armor (its almost immune to xbow bolts and of course is immune to poison), and has a lot of hp. Try to keep hammer users away from it, especially watch out for the acid-arm skaerders, and be careful about letting melee natives swarm it; it has a tendency to blast itself with its own AoE. It takes a lot of heat off of you and aegis, and can kill entire groups of natives every turn. Don't put mines near it, don't hit it accidentally (bursts, AoEs, electrokinesis, etc); you can turn it hostile. Aegis will sometimes turn it hostile with their grenades; such is life.
JET SKI
Fighting from a jet is ideal, especially if you are a ranged character. I won't go into what jet to use; there's other threads for that. The melee natives will ignore you entirely, you will be in the darkness (so they have penalties to shoot you and you can trigger ambush easily), and you have cover you can rush to at the end of your turn. You can much more easily put down AoEs where the natives leave the boats. You will be completely uninhibited from whatever traps or caltrops you put on the beach. You can always land if there is a need, and get back on your jet likewise. And if it comes to it, you have the easiest way to leave the map. This is not an option during the first invasion, obviously, since you won't have a jet.
PSIONS
Psionic characters have many great options for beach invasions. Plasma beam and cryo-orb are your main AoEs. Electro imprint is very useful to plug a gap or just kill an extra weak or wounded enemy. Cryokinesis can reach across most of the beach. Forcefield can block routes and act as a decoy target. You can run out and place yourself in stasis to draw fire and waste their buff durations. I won't tell you how to play your psi character, you should know by now, I'm just confirming that you will have a pretty easy time with invasions. If you run out of reserves, you can run to the top of the map and hide for a few turns to lose the "in combat" status and huff an inhaler (and use bandages or foods).
btw, if you have cryo-barrier, the patch of rocky-water in front of the SW boat can be blocked
PIRATE INVASION
And finally the pirate invasion. It can be avoided entirely if you managed to get the naval mines beforehand, but if you didn't, you are in for the hardest of the invasions by far. Domebangers have metal armor and are quite tanky, also thick skull. There will be multiple snipers, who can easily kill aegis, yahota, or even the naga. There are xbowmen with shock and incendiary bolts. There are grenade throwers. There are assault rifle users. It is very difficult, and you will almost certainly take some losses. The snipers should be your main targets, and the xbowmen are nearly as deadly to your allies. Stingballs will not be nearly as effective in this fight.
(images in next post)