Collect all six secret eggs in Banjo-Kazooie. Take the egg to Heggy's Egg Shed in Banjo-Tooie. Allow Heggy to hatch all the eggs. Complete the indicated task to unlock the corresponding Stop 'n' Swop II item.

And The Winner is...: Get the Gold Egg from the Banjo-Kazooie game pak in the waterfall at Spiral Mountain.
Better Than A Slap: Get the Silver Egg from the Banjo-Kazooie game pak to the right when entering Jinjo Village from Spiral Mountain using Grip Grab.
Calmer Chameleon: Transform into all of Humba's transformations (including Dragon Kazooie).
Heroic Failure: Die forty times during the Boss Replay Challenge.
Lucky Loser: Get the Bronze Egg from the Banjo-Kazooie game pak in a cracked grate after destroying it with a grenade egg and flying into it at Spiral Mountain.
Now Who's Boss: Complete the Boss Replay Challenge with a personal best score of fifteen total minutes or less.
Oh No, Not Again...: Have Heggy hatch all Stop N Swop Eggs.