Here is the full list of all 22 Wonder Boy Returns Remix achievements.
Kill first boss
Killed by boss's fire ball
Act V sign
Good job!
Clear Practice mode
Clear Normal mode
Clear One coin mode
Clrear within 1minute
Get 500000 score
Kill 500 monster
Kill 6 monster at once
Kill spider at once by charge shot
Destroy 50 rock and stone
Get 20 Tanya doll in one coin mode
Get hidden fruit 1-3 stage
Step on spring 5 in a row
Get Tomtom doll
Killed by goblin
After get ACHIEVEMENT of goblin, kill Goblin
Killed 5 time when Practice mode
Killed by collsion with boss's body
Drop and die in section of boss