You're meeting all the criteria, but are you playing in Practice mode? Currently I have it setup so you can't earn an S in Practice mode, since getting 0 deaths in practice mode doesn't really mean anything. (For example, players could just back out to the world map and re-enter the level each time they die to reset the death counter.) The original intention behind this design was for S-Ranks to be super tough to earn and serve as a longer-term, post-completion goal; unfortunately I didn't realize a lot of gamers like to perfect levels as they play them. My bad! For now, my advice is to not worry too much about the grades you earn. The system I designed needs some reworking, and I'm still figuring out the best way to tackle it. It will definitely be changed in a future update. And again, sorry about the difficulty of the mummy boss. It'll be toned down a bit in the first update. Spoiler BTW, after yanking the mummy's chain, you can also jump on his head instead of punching him. That may feel easier to pull off.