Anything below hard is boring.
I have completed nearly all missions on hard before finishing them all on lower difficulties.
For the first mission, you need accuracy and control. Simply set the team up with some automatic weapons like auto guns on specalisits, prototype on tech and medic could probably use an assult gun.
Second mission is the elevator. This needs some nice tactics to do easilly. Both medic and tech should have high accuracy damage and range weapons like the rifle. Both specials go auto gun and auto gun turret with tesla traps. Procede through the mission carfully advancing, the offhand of the tech + the specials will easilly handle everything. On the elevator place both sentuaries on top corners point into the midle of the platform so people can stand behind with no worry of getting hit. Place some tesla traps all around to make sure the enemies get slowed. Then get the medic and tech to just shoot the crap out of the stuff comming up the wall in the back with their weapons. Specials can try using their autoguns on the stuff as there is nothing else to shoot at but they are not the most effective in my experience. End result of this strat was me making it through hard more with 0 allied hits, 110 kills, 0 damage taken and a nice achievenemnt or 3.
Mission 3 is the first really open area. You will face a lot of badies swarming you. Although autogun senteries can help, they are not vital and you will discard them after the first hack sequence or boss. You are after any gun that deals massive area damage. Officers should consider a vindicator, and specials a mini gun on offhand. Onhand you need reliable point damage weapons to help keep enemies back like autoguns, flamethrowers or anything like that. Armor or gernades are best in this mission as you will not camp much and need the extra pushing power. Progress carefully to the house, making sure not to get too badly beaten up. In the house set up any sentaries and get 1 guy on evey entrance. The medic can probably shoot out the stuff to the right. Miniguns will totally decimate stuff comming through the doors. Progress carefully to the armored guy battle, if you have a sentary you can bring it with to help out but just go ahead and shoot the crap out of it, flaming it + explosives and it will die fast. Now the final part gets rough as you will have huge waves of aliens attacking you from both sides. The miniguns work wonders here as well and will probably let you push faster than the ship can fly.
As for the parasites, it is advisable to procede carefully or bring tesla armor with. One tap of hotkey 1 and you can have them quickly off with atleast some of your life remaining.
