Here is the full list of all 12 AST-Hero Playtest achievements.
Reach level 20
Kill the first boss
Kill the Mothership
Buy all upgrades available in a single game
Finish the game in easy mode
Finish the game in normal mode
Finish the game in hard mode
Finish the game in very hard mode
Finish the game in pyscho mode
Get into the shop with less than 5 health
Finish the game visiting the shop twice or less in normal mode or higher difficulty
Play AST-Hero before the official launch day