Here's the thing. These achievements don't stack. You honestly just have to play through the game on each difficulty. Try and make combos so you get the little "bonus" items. This game is HARD in the later levels, even if it appears easy at the beginning.
When you start out on the first couple of levels you will probably be able to beat them without using this save system. However, you'll want to save your progress inbetween sub-levels by pressing "b". This will mark down how many lives you have as well. When the levels start to get tough later in the game, you can hit start in the middle of a level, quit out of it, save in the process, and then return to that point in the level. If you die in a level, simply hit your xbox controller guide button, quit to dash/the arcade compilation disc if you have it on that, start up the game again, and resume from your last save point. If it wasn't for this feature, I never would have been able to beat the later levels - you can do this multiple times per level keep in mind.
If you lose all of your lives, you will be forced to restart the level and will lose your sub-level progress.