Here is the full list of all 19 Invasion achievements.
Kill self by nuke
Kill self
Kill 100 ufos
Kill 500 ufos
Kill 2k ufos
Kill 10k ufos
Kill 50k ufos
4-9 kills per time
10-20 kills per time
21+ kills per time
Firing accuracy <= 10%
Firing accuracy >= 95%
Firing accuracy == 100%
Finish level with 1hp
Finish level without damage
10 deaths in row
Use 9+ nukes per level
Use 21+ nukes per level
Use 666+ nukes