While playing a one-player campaign, hold L1 + L2 + R1 + R2 + Select then press Start + X.
To Kill a Battleship
The easiest way to kill a battleship is with a submarine. As soon as the battle starts, DIVE! When you dive, a helicopter will come out and use sonar to find you. You should make your way under the other ship. While staying under him, pump out torpedoes like heres no tomorrow. In this way he should be destroyed fairly easily.
Trash a Carrier with your PT Boat
When the battle starts, let him target you and launch his planes. Then, extend your hydrofoils and turn straight into him. His planes will miss you (most times), and won't be able to land when he's turning away from you. Keep turning with him as you light him up with torpedos.