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(Note: All the tricks listed can't be performed by all the racers.)

No Hander: L2 + ⬇

Lookback: L2 + ⬆

No Footer: R2 + ⬆

One Footed Can-Can: R2 + ⬇, ⬅

Nac Nac: R2 + ➡, ⬇

One Footed Can-Can and One Hander: R2 + ⬋

Recliner: L2 + ⬉

Airwalk: L2 + ⬈, ⬊

Saran Wrap: R2 + ⬋, ⬇

Decade: L2 +⬊, ⬇, ⬋

Heel Clicker: R2 + ⬅, ⬆

Parallel Can-Can: L2 + ⬅, ➡

Knockout: L2 + ➡, ⬅

Nose Dive Suicide and No Hander: R2 + ⬊

Nothing: R2 + ⬈, ➡

One-Handed Superman: R2 + ⬉, ➡

BackFlip: R2 + L2, ⬉, ⬆, ⬈

Various Tricks: R2 + L2, ⬉, ⬆, ⬈ (Only users: Gio, Tracey, and Travis.)

(Tracey can't perform the Airwalk, Decade or a BackFlip.)

(Gio can't perform the Saran Wrap, Nothing or a BackFlip.)

(Travis can't perform the Nose Dive Suicide and No Hander, Recliner or a BackFlip.)

[Source: the manual]