While you are grinding on a rail do a double jump.
To Unlock Battle Arena, earn all the Grades, Then you should get the Master Grade. The Battle Arena Will be open at Robot Beach.
Hold R1 and press triangle four times.
Then let go of R1 and hold L1 while pressing triangle ( twice ). Next hold L1+R1 and press triangle, circle, triangle.
Push start during the game to pause. Keep R1 pushed down, then give the following combination: square, square, square, circle.
Now let go of R1 and keep L1 pressed, pushing triangle twice. Let go of L1 and press R1 again while pushing square twice.
Hold R1 + L1 and press circle, square, circle, triangle ( twice ), square, circle, square.