Here is the full list of all 15 Squad 51 vs. the Flying Saucers achievements.
Finish the first level.
Achieve three stars in the first level.
Finish the last level.
Achieve three stars in the second level.
Achieve three stars in the third level.
Achieve three stars in the fourth level.
Achieve three stars in the fifth level.
Achieve three stars in the sixth level.
Achieve three stars in the seventh level.
Achieve three stars in the eighth level.
Achieve three stars in the ninth level.
Achieve three stars in the tenth level.
Achieve three stars in the last level.
Achieve the total score of 1,000,000.
Achieve three stars in all levels.