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