Successfully collect all Pokemon in either Pokemon Ruby or Pokemon Sapphire to unlock an alternate border in adventure mode.
Egg
The egg you get is NOT a secret Pokemon. It is either a Swablu or a Zigzagoon that learns moves it shouldn't. When my Swablu hatched, it knew False Swipe. Don't bother hatching them, they're nothing special.
Pichu with Surf Egg
Store 1499 Pokemon to get Pichu with the Surf Egg.
Skitty with Pay Day Egg
Store 500 Pokemon to get Skitty with the Pay Day Egg.
Swablu with False Swipe Egg
Store one Pokemon to get Swablu with the False Swipe Egg.
Zigzagoon with Extreme Speed Egg
Store 60 Pokemon to get Zigzagoon with the Extreme Speed Egg.
All attributes...