In hardcore mode there is no checkpoints, and one hit kills you. This will be the thoughts of the achievements to get in this game. Hardcore mode will open as soon as you complete normal mode. You have to complete all levels, incl. the secrets ones. I found it easies to give the map a try, many times you can get through without dieing. If you're struggling, look up a video on the Internet (see link) to see what is coming up. Here is a web-page where there is a writing + video guide of each level, so you know what is coming up.http://www.gamefront.com/ms-splosion-man-walkthrough
EDIT: I notice there was missing 2 videos on the homepage. World 3, level 6 and last boss fight. Added both down under.
WARNING LAST VIDEO CONTAINS SPOILER OF LAST BOSS (But if you started hardcore, you already know it)
Credit to Mitchell from Gamefront, alot!
Credit to RatingPendingGaming for last boss fight video.