Free Flow Action
These are the "flashy" actions Nomura has mentioned in the past. By pressing Y, you can make your character kick off walls, swing around poles, slide down rails, and so-forth. You can string together these actions. You can also connect into other moves -- pressing A or a powerful attack, or B for a jump.
Reality Shift
When you're attacking enemies, objects and enemies will sometimes be highlighted with a cursor. Press X and A simultaneously, and you can perform special attacks through the lower screen.
Dual Link
In DDD, you fight along side demons known as "Dream Eaters." In the TGS demo, you start off with two of these in your party. As you build up a gauge, the Dream Eater's icon will begin to flash. Tap the icon on the lower screen, and you'll be able to do a team attack. You can also team up with both Dream Eaters simultaneously.