For X-Com: UFO Defense. I think all of these are possible, though I don't have them all yet.
Survivor: Win a terror response mission involving Chrysalids with only one surviving friendly on the map.
Sisters of Sorrow: Demolish an alien base with an all female team. (Was "Mars needs women" but I decided that would be too spoliery.)
Recon by Fire: During a night mission, set an alien on fire that was out of LOS.
The Undying: In one month, resolve at least 5 incidents using the same response team with no civilian or military casualties.
Twitch: In one turn, kill 2 aliens with reaction fire from the same soldier.
Mundane Levitation: Destroy the ground floor of a building, but leave the upper floors.
Pacifist: Win the game without killing any alien operatives, any soldiers, or any civilians. This involves exactly one kill. (Civilians, soldiers, or aliens killed by aliens do not count.) (The "final boss" needs killed, that's why the "exactly one" part. It is not clear if "researched" live aliens end up dead at the end, but you need to interview at least 2 of them so that doesn't count. There is no essential research from dead aliens, and some of the terror creatures probably qualify as machines, particularly those which cannot be stunned.)
Xenophobe: Win the game without equipping alien weaponry on any soldiers or craft, and without using any items of alien manufacture. (So no alien grenades, even though you don't really equip them. I am not sure if a human-manufactured mind probe should count against this achievement. Researching alien tech is O.K., since you can't win the game without it.)
No Fear of the Dark: Respond to a UFO during night with no flares or incendiary weapons. (Terror mission doesn't count because it has street lights. Not that it helps much.)
Urgent Delivery: Purchase ammo for a base that has no usable weapons or ammunition. (Base must have 20 or more solders and a hangar).
