The trick is to destroy the launcher as quickly as possible.
Make a bee-line for the right side once the rockets start to rain down from above, Spin attacking the rocket launcher first, followed by mangling the Casino manager in the blue suit (perform the button pressing when prompted to take him down). Now mop up the remaining troops and grab all the food that is around, heading into the final area. Phineas and Barnaby will be the final obstacle to overcome, so use Spin attacks to hurt them, grabbing the corn they drop to keep the snack meter full enough, draining both low enough so the button combination finishing technique can be utilized, taking both down. They drop more than enough health and corn, so they should not pose a significant problem for Peter