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