Defeating Princess:
Run up against the well and shoot when you are fighting the giant eye monster princess and she will not be able to get hit.
Defeating the Tank:
Go to any ramp and stay out of the tank's sight. Use the Telekinetic Glove to take the ammunition when it spawns and attack the tank with rockets.
Hats:
Enter one of the following names as a player in the 'Options' menu then select 'Submit'. If the correct code has been entered you will hear the sound of a foghorn to confirm correct entry. The corresponding hat will be unlocked in the 'Hat' menu.
Hat 2 - (Tom Fulp) TomFulp
Hat 4 - (Blonde hair) Cletus

Hat 5 - (Red hair) April

Hat 7 - (Jheri curl) Superfly

Hat 8 - (Pirate bandana) Goodman
Hat 11 - (Top hat) Grrl

Hat 12 - (Diamond tiara) Abe

Hat 13 - (Daisy headdress) Princess or Betty
Hat 14 - (Dick Tracy hat) Dandy