Hyper Punch Mode
At title screen, hold L1 + R1 and press Left, Right, O, Up, O, Right, Left.
100% success rate. 

Original Pitfall Mini-Game
At title screen, hold L1 + R1 and press O, O, Left, Right, O, Square, X, Up, O.

Pitfall 2: Lost Caverns Mini-Game
Buy all items from the Shamans and collect all Idols.

Go to: Pitfall: The Lost Expedition Info Page | nGaming Home Page.