Here is the full list of all 16 Slashy Hero achievements.
Get 10 points in the Infinity level
Get 100 points in the Infinity level
Defeat the Ghost Lord
Wear 3 costume parts
Wear 2 costume parts
Wear a costume part
Get a 10 kill combo
Defeat the Skeleton Lord
Get 500 points in the Infinity level
Get 1000 points in the Infinity level
Get 2000 points in the Infinity level
Get 3000 points in the Infinity level
Get a 20 kill combo
Get a 30 kill combo
Complete 48 levels without dying
Get +30 in all stats without costumes