For the hard badge, get the handstand, max out everything (except groupies cuz they don't help) and try to get your rocket to push you up as straight as possible, while doing handstands as quickly as possible. And try to bounce as you land to get that extra handstand in. Didn't take me long to get the hard badge that way.
Could you put in an autoregister feature, where it automatically saves where the shops are? The last time I used wings was around lvl 19, so it put me at lvl 9. I was in the 80s, died, and it didn't save anything that I accomplished through 70 floors... Put me back at floor nine with almost no artifacts...
Hm. Triple S rating first time through. lol 1 healer, a unique knigt, unique soldier, and unique archer. Conquer the territories asap, do as many quests as possible, and stick with the expensive upgrades is what I did, maybe it will help.
There should be an exit from battle button on the challenges, especially for the "Distraction" one. I really don't want to watch the "shield" run into the "dragon" for 10 minutes.....