Here is the full list of all 34 Tetra Tactics achievements.
Augment a card
Complete your first run
Use a hero power on an enemy card
Get 10 combos in a run
Get 20 combos in a run
Get 30 combos in a run
Use 5 potions in a single run
Use 10 potions in a single run
Use 15 potions in a single run
Have a card with all 4 symbol types
Convert all numbers to symbols in your deck
Capture 8 cards in a single move
Capture 4 cards before comboing
Win a match after getting comboed three times
Win a match with no enemy cards remaining
Play a match without any of your cards getting flipped
Gain back 20 supply in a run
Have 10000 gold during a run
Have a deck consisting of all augmented cards
Beat the first boss
Beat the second boss
Beat the final boss
Draw every non-boss match
Beat the game without using upgrades
Beat the game in less than 20 minutes
Beat the game without spending any gold
Buy every perk
Beat the game with Curse Level 1
Beat the game with Curse Level 5
Beat the game with Curse Level 10
Beat the game with Curse Level 15
Beat the game with Curse Level 20
Beat the game with 5 different heros
Beat the game with no perks active