NO1KEV already said something really important about the game - make sure you get the "saved" sign in the top right corner after you've finished a stage.
I want to add something else about this achievement which might be important as well:
A) the "I Need MORE Healing" achievement might take longer than you think. It unlocked for me after two complete playthroughs on Normal Mode and one playthrough on Heroic Mode. So don't worry too much, it will take some time.
B) the "Explorer" achievement can be a little tricky, it might be bugged. On my third playthrough I finally got this achievement although I've been through every hidden wall before (more than once!). So, if you face this problem like I did, just keep playing the game and enter every hidden area over and over again. This might be again related to what NO1KEV said, but I always completed the stage and got the "saved" sign on the loading screen.
After you completed every other achievement, the "Completionist!" will obviously be yours and it will pop right away.