Here is the full list of all 15 1979 Invasion Earth achievements.
Five whole killer minutes in Survival Mode
Four whole minutes in Survival Mode
Smashed an alien
Defending Old Blighty
Two whole minutes in Survival Mode
Defending Moscow
Defending Tokyo
Defending Toronto
Defending Paris
Defending New York
Destroyed your first alien mothership
The proud owner of five lives.. nice
Completed Stage with at least 300 Human Survivors
Finished all stages in Skill Shot Mode