Bonus Boss Battle:
Wait for the credits to finish at the end of the game.
Max your Aeon Pulse to level 5 and set it so that you can do Radial Flare. This weapon usually kills in one hit and could easily clear out rooms.
Chapter 1 Warp Pipe:
You must find 6 hidden buttons on this level.
(1) Repeatedly hit the locker in the starting, first room until it disappears.
(2) Behind the pillars to the left of the first room.
(3) Go out the first room in the same direction in which you entered the level. The button is near the door with the flame in front of it.
(4) Look behind the left locker in the second escape pipe room.
(5) Check behind the pillars in the second escape pod.
(6) On a door on the first section of walkway over the large room with people running below and ships flying above.
After you have found the sixth button, just turn around and follow the opened path to the secret tunnel. The left pipe goes to an intermission sequence, the middle pipe warps you to the top of a building in New Bahn, and the right pipe is another intermission cinema.
Chapter 4 Warp Pipe:
You must find 6 hidden buttons on level B:
(1) When you first start to hit the black object in the all in front of you.
(2) You will then pass under a large gun. Walk into the open area and destroy the black object opposite the area entrance.
(3) Go up the small ramp and wait until a pair of bridges appear next to a second large gun. Use a charged jump from the bridge to reach a platform above the large gun to access a hidden room.
(4) Keep going until you get to an area with three doors that enemies are appearing from. Go to the large door furthest back from the other two that is under a turret. Follow the tunnel.
(5) and (6) Get to the place where you have to hit a switch to make a bridge. While walking across the bridge, look to the right and find a space with a pair large explosive objects in it. Destroy both of them.
Thanks to Revolution readers S.A.M. Gunny_joe, ERASURE, o0olooko0o, betty79, and David S!