This achievement sounds worse than it really is. Yes, you do have to beat the game with only two hearts but as long as you keep using Bubble Shields, Super Pike Balls and Super Monster Milk you'll be fine.
I strongly advise you attempt this on New Game+ (Pirate Mode) which allows you to start the game with all Pirate items as you can skip a lot of sections of the game thus minimizing the potential for getting yourself killed.
The main thing want to do is get your hair and weapons upgraded as fast as you can to you can shred through bosses in no time.
Another achievement requires you to complete the game in a 100% Speed Run. If you plan to go for that achievement I would advise you do this one at the same time.