Here's my ideas.
First levels:
Onua: you have to carve a path through destroyable scenery while fighting rahi.
Tahu: Idunno
Kopaka: You have to shield-slide down the mountain while a muaka shoots snow and ice at you with its tread.
Lewa: you have to swing from vines and jump so you can get onto a gukko a matoran is riding above you.
Gali: swim away from takea sharks as fast as possible, and hope you reach ga-koro before you get eaten.
Pohatu: Generic fight the monsters till you get to Po-koro.
Once you reach your Koro, the turaga will send you on quests (E.G. "Defeat twenty rahi", "Find Macku's Hewkii Plush", "Defend the statues"), the rewards being stuff like bamboo disks, madu cabolo, and hints on the wherabouts of the masks(E.G. "Look on the tallest monument" for mount Ihu).
Also, Achievement ideas:
Pyromaniac: Complete all of Tahu's levels.
Hurricane: Complete all of Lewa's levels.
Ice Cold!: Complete all of Kopaka's levels.
Aquanaut: Complete all of Gali's levels.
Great Stone Dragon!:Complete all of Pohatu's levels.
Idunno for Onua
Duckies: complete the Mangai levels
Hunter: Defeat "x" amount of rahi.
War they Want: Defeat "y" amount of rahi.
Fight to the Finish: Defeat ALL rahi.
Burninator: Destroy all destroyable scenery.
Savage: Defeat "X" Rahi with only physical strikes
Sniper: Defeat "X" rahi with only elemental strikes.