Here is the full list of all 35 RADical ROACH Remastered achievements.
Beat On Normal Mode
Beat The Game
Beat On Hard Mode
Beat W4-Boss
Pop It's Mask
Beat W4-L5
Beat W4-L4
Beat W4-L3
Beat W4-L2
Hit The Mantis Baby
Beat W4-L1
Beat W3-Boss
Beat W3-L5
Beat W3-L4
Beat W3-L3
Beat W3-L2
Beat W3-L1
Kill 100 Fire Bugs
Beat W2-Boss
Beat W2-L5
Spit On The Rock
Beat W2-L4
Beat W2-L3
Find The Hidden Path
Beat W2-L2
Beat W2-L1
Beat W1-Boss
Beat W1-L5
Kill 1000 Mosquitoes
Beat W1-L4
Beat W1-L3
Kill 1000 Poppers
Kill 500 Mosquitoes
Kill 100 Mosquitoes
Beat W1-L2