Here is the full list of all 19 PARSE ALLY achievements.
Get red rarity weapons
Get purple rarity weapons
Get yellow rarity weapons
Get kusarigama
Get bow
Earn Level 20
Earn Level 30
Earn Level 40
Buy buff
Buy an item
Pass at least eight waves in a cage
Pass at least thirteen waves in a cage
Level up companions to 250 or more
Level up companions to 500 or more