Many Bosses such as Manboroth will give you a mini-game when you defeat them on Level 3. Some bosses will also give you eggs on Level 5.
Fah Zakpon (Farming) mini-game: Defeat Centura Level 3.
Kon Kimpon (Mountain) mini-game: Successfully complete Nanjaro Hill Training Course Level 1 (only 1 cannon appears).
Pan the Pakapon (Tree) mini-game: Successfully complete Juju Jungle Training Course.
Rah Gashapon (Cooking) mini-game: Defeat Phoeniti/Fennichi Level 3.
Shuraba Yapon (Dancing) mini-game: Successfully complete The Sky Castle where a God Lives (where you first see Dark Hero).
Ton Kampon (Blacksmith) mini-game: Defeat Manboroth Level 3.
Tsun Tunpon and Tsuku Tsukupon (Alchemy) mini-game: Defeat Manboth Level 3.