As soon as you start getting money from killing Volgara, try to put as much as possible into making your character and Vavel more powerful by purchasing new attacks, thicker armor, and more ammunition for your weapons. Vavel's power is average at the start of the game, but if you build it up completely, it will be combat superior to all of the other enemies and Meganites, including Osmodeous.
To get a better view and control of your mech while it fights, use your Gravity Boost (on the "Hero mode", hold Circle) and boost your way to the top of a nearby building. You can now get a much better view of your mech and the fight that it is in.
Faster intermission sequences
Hold Start during a break sequence to fast forward it.
Finish the game to unlock all robots in versus mode.