This one will come easily over time.
As you progress through the game you'll find Imaginite Chests everywhere. You can get them from:
1) Playing through levels
2) Getting Objective Stars
3) Winning Skystones matches
4) Winning Arena Rounds
5) Winning Gong Challenges
6) Completing Bonus Goals
7) Defeating Random enemies on the M.A.P.
8) Connecting all Gems in a lock puzzle
9) Completing a Troll Radio challenge
10) Chasing a snail
11) Finding them sitting out in the open
12) Placing a new Imaginator/Sensei on the portal
13) Completing Side missions after the main story
14) Returning books to the Academy
15) Down a rat hole
16) Buying them with money (
DON'T
)
As you can see, the chests are numerous and plentiful. Just speeding through the story should get you enough chests to get the achievements.
If, however, you just want more chests to get more goodies (or trying to get Ultimate gear), the quickest route becomes available once you've unlocked the Dragon's peak level:
Take Sharkfin's ship up to the island, grab the dynamite, rail grind back down to the main island, and make a mad dash to the well by Sharkfin's ship. If you're fast enough, you'll blow up the well. Inside is 300 gold and 2 chests. Leaving and reentering the M.A.P. (best by the arena right next to the well) resets the well allowing you to get two more chests, allowing you to rinse and repeat as long as desired.