Here is the full list of all 31 Peglin achievements.
Defeat the Mole Boss
Leave an enemy with just one health point
Defeat the Ballista Boss
Fully clear a pegboard
Defeat the Slime Boss
Deal just enough damage to kill an enemy
Defeat the Wall Boss
Defeat any boss on the first turn
Die during an event scenario
Deal exactly one damage
Deal 9000 or more damage in one shot
Hit 1000 pegs or more in one shot
Bramble an enemy for six turns in a row
Defeat Avogadro's Tree before entering the Castle
Defeat the Animated Ruins
Inflict 50+ stacks of poison onto a single enemy
End a battle with 100 Ballwark
Complete Cruciball Level 10
Complete Cruciball Level 15
Defeat Betsy the Leshy
Get three Bramballs stuck in Leshy's vines at the same time
Win a run with two eggs in your satchel