Here is a link to maps from the game. The final area has no Chests or Life Cubes. Also keep in mind you don't need to collect Medkits for the achievement.
I didn't make these maps, apparently the devs Woblyware did, so thanks y'all! Someone posted this on the Forum for this game, but I figured it would be helpful to the next guy for me to share it here as a solution.
I recommend copy pasting these on MS paint and crossing them off as you find them and make little notes for which ones you need to come back for when you have the right ability. I use this technique with a lot of games and it's helped me a lot over the years.
https://imgur.com/a/ayDkhWB