Here is the full list of all 24 UFHO2 achievements.
Beat all the Hard Situations
Enter two Loopholes in one turn
Beat all the Medium Situations
Use two Gem Teleport in one turn
Beat all the Easy Situations
Complete the Story Mode
Unlock powerups to be consumed
Unlock all powerups to be used on Rooms
Unlock Gooo from World of Goo
Unlock all stages in Jeevil missions
Unlock Gish from the Gish
Unlock all powerups to be used on Sector gears
Get two Gems in one turn
Unlock all 4 original alien races
Unlock the Critters from Super Crate Box
Unlock the Commander from Bit.Trip
Unlock all stages in Gooy missions
Unlock the Cortex from Cortex Command
Unlock the Hexabot from Blocks That Matter
Get a Gem in your first turn
Get 100 total Gems
Get 300 total Gems
Play 30 matches
Play 100 matches