I know, it's because I'm really desperated to reunite those fragments. I bet there is only one missing.
Wait, go talk to her again. I had them all, when I first saw her, but THOUGHT I didn't have enough because she has to talk about the fragments first. Talking to her again did the trick.
Ah ha ha ha. Nice job...you're ALMOST making me quit. However I won't give up that easily! (That is if I can get to those damn stairs >.>)
Oh, by all means, do it when and if you can. Just expect it to stop being fun after reaching floor 30. As long as you skip the floor 21 boss, it paces well until floor 25, which is the first grind wall. It's not too much worse than the ones you've experienced so far, so you'll move on in no time. From there, you can basically run to floor 30 with only one troublesome fight, and from there, it's ALL grinding. Get used to fighting bikini clad liliths and black knights, because you'll be fighting them for as long as it took to reach that point and then some.