One of the hardest parts of this achievement is unlocking the mode that you need in order to complete it. I recommend legitimately playing through the first four modes, since you need the levels. Using this video guide I found will help you get through the tougher modes, Bat Princess and Naturist Princess Sarah, where your primary attack is pretty much useless. You can also use this to finish the final castle, but you will not unlock the achievement for defeating Greater Lilith unless you legitimately defeat her in the final game mode, Vampire Princess Sarah. I included this in my advice guide for that achievement. These exploits are tricky, but they are useful tactics to succeed.
Video credit and ownership belongs to Dr Casual. He makes them look easy, but they may take practice and many attempts to get right. The hardest ones are at the ends of Castles 2 and 3. For the last part of castle 2, after making your final out-of-bounds jump to the right and quickly holding left, a well-timed secondary jump is helpful for getting into the end alcove.