100%, No GB Transfer - NEW, FASTER (5 bonus 1 replay):

Remove memory card before winning Castle.

• Beat Coaster Lake or Bomber Circuit
• Finish Beach Side (+100 coins) and Dyna Mountain (+100 coins)
• Buy Hyper Louie, 2 P-Bombs, beat the rest of the normal tracks. (credits / save screen)
• Finish Beach Mirror (+100 coins) and Dyna Mirror (+100 coins)
• Buy Black Louie, 2 P-Bombs
• Finish Dyna Mirror (+100 coins) You should have 19456 or more coins (rounded up 19460, 19480 if you want to buy a small heart before Star Road to dodge items). If you have 19410 or 19360, sell 1 or 2 P-Bombs. If you have less than that, you'll have to play an extra bonus lap (Bomber Circuit non-100c while grabbing as much coins as you can usually gets the job done).
• Beat the rest of the mirror tracks (credits / save screen)
• Buy all Tirras, use King Tirra to beat Highway Star Road (buy 1 or 2 small hearts if you have 5676 / 5696 or more, to dodge items easily and regain stamina).

The sum of "time left" at the end of the bonus laps must add up to 256 (assuming 4 P-Bombs) Good times on those bonuses are: 76, 72, 28, 52, 52. So you can make around 24 seconds of mistakes. If you're uncomfortable with this, either don't buy the P-Bombs or do Ski Course (normal) Bonus rather than Beach (normal) (Not Recommended).

Credits to arichan for posting a comparison video, which led to a much faster 100% no transfer route.

Mirror Castle End (or slower 100% NGBT, which has 4 bonus 1 replay):

Remove memory card before winning Castle.

• Buy 2 P-Bombs, finish: Lake - Beach - Circuit - Ski+100 - Dyna+100

• Buy Hyper Louie, finish Star Express and Castle (credits / save screen)

• Buy 2 P-Bombs, beat the mirror tracks, doing Star Ex (+100 Coins) before Dyna (credits / save screen, mirror castle END)

• Finish Castle Mirror (+100 Coins) again

• Buy all Animals, use King Tirra to beat Highway Star Road (buy 1 or 2 small hearts if you have 5676 / 5696 or more, to dodge items easily and regain stamina).

100%, Unrestricted:

Save your file on slot 4 beforehand

• Beat Coaster Lake (+100 Coins), with 66 or better time left (%) Spam X, quitting to Options Save 4x (4 - 5 - 1 - 2) - - (%) Bank, transfer (4 - 5 - 2) to 1 Options, Load Save 1 - Don't forget this!!! Save 4x (4 - 5 - 2 - 3) Bank, transfer (4 - 5 - 2 - 3) to 1 Options, Load Save 1 - You should have 31200 gb or more.
• Buy Black Louie, 2 P-Bombs Remove memory card before winning Castle.
• Beat Normal Tracks
• Use Black Louie again, buy 2 P-Bombs, beat mirror tracks (credits / save screen)
• Buy all Tirras, use King Tirra to beat Highway Star Road (buy 1 or 2 small hearts if you have 5676 / 5696 or more, to dodge items easily and regain stamina).

(%) if you get under 66, save one extra time in this step (slot 3), and transfer it to 1 as well. You can have 50 slots in your save file (done by holding L1 + L2 + R1 + R2 + Select + Start and pressing Circle to create new game data), but you only need a 5-slot save file, even if you don't get 66 on lake bonus.

Some race orders are arbitrary, others are not (except for using Hyper Louie for the last two normal tracks in No GB Transfer, my testing indicates it saves 10+ seconds). Feel free to use the order you want otherwise, either for better comfort or fast menuing (which doesnt have much time variance). The routes assume you're doing louies as your main characters. You can do King Tirra on 100% and 100% NGBT, you would have to check if the money works with choosing Super Tirra > Hyper Louie.