Getting to the place where the second round takes place | 13: Devil's Dalliance DMC: Devil May Cry Guide

After a battle stand on a new plate and use Eryx. Now start jumping onto platforms in front of you. Notice that every shelf is moving. Knowing that, jump and use Angel Boost when the one on which you're standing reaches its peak.

I recommend to use platforms on left side, because it's easier to jump onto them. Don't overuse Angel Boost, because it's easy to misland, the platforms are small. When you reach the highest platform (screen above) use Angel Lift on a latch what transfer you where the second round begins.