Unlocks
Some of the trickiest things to unlock require perfect play, lots of luck, or just finding something very well hidden. This page will try to assist in the last part by providing photos and instructions on different unlocks. Match Race is very useful in unlocking challenges, as you can select the items you need to make sure only those necessary will appear (usually Pogo Spring or Gachabom).

Shrines
Several challenges require you to find an ancient shrine and play a melody. The "melody" comes from your horn (which can be activated with the "look back" button) and only activates when you have the Mystic Melody equipped, a pet that is obtained from Lost Colony. The shrine must be behind you as you look back to activate the shrine. A video of how to obtain the Mystic Melody is here: Thanks, AlsoIMainYoshi!

Northern Districts (Unlock Headdy)

The shrine is on a ledge near the bridge. Use a Pogo Spring or other speed boost to launch off the edge of the bridge (you can climb up the edge - the jump point is just after an item bubble with a Bomb).
Storm Rig (Unlock Follower Aquis)

Turn around after the drop and you'll be able to drive right through this grating. A caution-tape colored lift will take you to the Shrine if you wait on it.
765 Stadium (Unlock Azusa Miura)

Use a speed boost facing the opposite direction from the sneaker panels at this curve to leap over the guard rails. If close enough, the shrine can be activated from the track.
Azure Axiom (Unlock Ecco)

Use a Sneakers or other boost to increase your speed coming up to the gray Trick Springs and trick forward to reach the second level and start Lap 2 on the higher area. Spin Dash onto the yellow Trick Springs and trick left to get into the opening with the Shrine.
Melty Manor (Unlock Arle)

Instawhip the switch and the door opens, and you can go through that door that opens up. Go slowly on the upper floor along the right and into the next door to find it waiting at the end of the dark.
Avant Garden (Unlock NiGHTS)

Turn to your left after entering the castle and use a Pogo Spring to get to this secret area. The shrine is inside of a small hedge maze.
Star Light (Unlock Follower Uni-Uni)

Turn to your left after the big jump at the start.
Haunted Ship (Unlock )

Lob a Gachabom to hit the switch in one of the ship masts. A door will open up right after this point to the left.
Hidden Palace (Unlock Zipp)

Find and hit this switch along the side of the track after the lift to open this door much further along.
Darkvile Castle 2 (Unlock Wonder Boy)

There is a switch to the right of the track that opens up the gate to the right of it. It's tricky to hit - try lobbing a Gachabom.
Regal Ruin (Unlock Tails Doll)

Drive across the water to reach the island with a structure on it, then spin dash into the grate to reach the Shrine.
Emerald Hill (Unlock Surge)

Drive behind the first waterfall to find the Shrine.
Nova Shore (Unlock Follower Manegg)

Boost into, or just drive into, the pufferfish/bubble enemies to reach a ledge. Following the cave will take you way off the map to the Shrine.
Las Vegas (Unlock )

Turn to the left once you see this "Party Room" sign and you'll see an open room with the Shrine.
Collision Chaos (Unlock Follower GA)

There is another opening near the shortcut at the end of the half-pipe. Use a Spin Dash and a Sneaker to reach it and enter the room with the Shrine.
City Escape (Unlock Chao)

The Shrine is just off the course; no special items or techniques are needed to find it.
Coastal Temple (Unlock Tikal)

After the first tunnel, turn to the left and you'll see a lot of pillars. Drive between them (you may need rocket sneakers) to reach a tunnel, beyond which is the Shrine.
Lost Colony (Unlock Maria)

Turn around after a big drop. Use sneakers (maybe 2) or a spin dash and sneakers to launch off the ramp to a platform with crates and the Shrine.

Passwords
Red Ring Rico: Unlocks ???
idclip: Unlocks ??? (30-year old password)

Other Secrets
Hidden Palace

To reach Hidden Palace Zone, you must fall down into the northwest corner of the second pit about halfway around the course on the third lap of the Grand Prix race. Turn left when you are driving fowards to reach it.
Adventure Example
Enter Espresso Lane on Match Race with only a Pogo Spring, then spin dash up the side of the course to get on top of the bridge. Drive down and use the Spring to launch up the tunnel (using a down-trick). Use the bananas to trigger the switches and make it to the end of the tunnel, and you'll fight Blend Eye. (Tip: Restarting the level at this point will send you back to the start of the fight! If you let the No Contest screen run to the end, you'll have to do the whole puzzle over again!) Video: Link