Here is the full list of all 34 Bucket Knight achievements.
Beat the 7-1 stage
Find the Holy Grail
Beat the 6-4 stage
Buy a minigun
Beat the 6-3 stage
Beat the 6-2 stage
Beat the 6-1 stage
Beat the 5-4 stage
Beat the 5-3 stage
Beat the 5-2 stage
Beat the 5-1 stage
Beat the 4-4 stage
Beat the 4-3 stage
Beat the 4-2 stage
Buy a shotgun
Beat the 4-1 stage
Collect 10000 gold
Beat the 3-4 stage
Beat the 3-3 stage
Beat the 3-2 stage
Beat the 3-1 stage
Buy a machinegun
Beat the 2-4 stage
Beat the 2-3 stage
Collect 5000 gold
Beat the 2-2 stage
Beat the 2-1 stage
Beat the 1-4 stage
Beat the 1-3 stage
Beat the 1-2 stage
Collect 1000 gold
Get poisoned by cheese
Beat the 1-1 stage
Start a game