Here is the full list of all 20 Arcade Game Series: GALAGA achievements. It takes around 2-3 hours to unlock all of the achievements on Windows.
Shoot down a red captured Fighter!
Reach Stage 10 and view the stage emblem!
Find the stingray that appears in battle!
Find the Scorpion that appears in battle!
Form a Dual Fighter!
Find the Dragonfly that appears in battle!
Find the Mosquito that appears in battle!
Find the Galboss that appears in battle!
Find the Blue Spaceship that appears in battle!
Escape from a Boss Galaga's tractor beam!
Get a 70% or higher hit rate on Stage 10 or above!
Get a Perfect Bonus on the Stage 11 Challenging Stage!
Get a Perfect Bonus on the Stage 15 Challenging Stage!
Get a Perfect Bonus on the Stage 19 Challenging Stage!
Get a Perfect Bonus on the Stage 23 Challenging Stage!
Get a Perfect Bonus on the Stage 27 Challenging Stage!
Get a Perfect Bonus on the Stage 31 Challenging Stage!
Without forming a Dual Fighter, get a Perfect Bonus on a certain Challenging Stage!
Reach Stage 20 and view the stage emblem!
Reach Stage 30 and view the stage emblem!