Crash Nitro Kart

Collect the indicated amount of CNK tokens in Story mode to unlock the corresponding Gem Cup.

Blue Gem Cup
Collect 4 Blue CNK Tokens.

Green Gem Cup
Collect 4 Green CNK Tokens.

Pink Gem Cup
Collect 4 Pink CNK Tokens.

Red Gem Cup
Collect 4 Red CNK Tokens.

During this track you will reach three boosts in a row. On the third boost, jump to the right. You should land on a platform. Use this if you want to cut that corner.

Unlock Pura by doing 50 consecitive boosts in a track in Adventure mode with the Bandicoot team.
Unlock Fake Crash by doing the same thing, but using the Cortex team.

Here's an easy way to do it:

If you go onto any ordinary track you won't be able to do consecitive boosts. You need to choose the track HYPER SPACEWAY.

In Hyper Spaceway there is a blue, transparent pipe in the last part of each lap.

1) Do 2 boost turnings by pressing R1 once and then quickly pressing right. Then press L1 twice as the speed dial changes from green to red.
2) Then quickly jump. That will make 3 boosts.
3) Repeat steps 3 and 4 until you make 50 boosts.

You can unlock N.Trophy by getting a lower time than him in each track.

While playing each of the 13 race tracks in Race Time Trial:

1) Use all the shortcuts that are possible.
2) Play single races before you play Race Time Trial and find all the shortcuts in each track.
3) Always use Velo while playing Race Time Trial because he is the 2nd fastest racer after N.Trophy and his turnings are quite good.
4) Keep doing boost turnings and collect Wumpa fruit boxes that will make you faster.

Accomplish the following tasks to unlock the corresponding FMV sequence at the 'Extras' menu.

Team Bandicoot
Challenging Krunk: Win three trophies.
Krunk Loses: Get one key.
Challenging Nash: Win six trophies.
Nash Loses: Get two keys.
Challenging Norm: Win nine trophies.
Norm Loses: Get three keys.
Challenging Geary: Win twelve trophies.
Geary Loses: Get four keys.
Challenging Velo: Get four keys.
Losing to Velo: Get four keys.
Defeat Velo without 100%: Get four keys.
Defeat Velo with 100%: Get four keys, thirteen Relics, and one Scepter.

Team Cortex
Challenging Krunk: Win three trophies.
Krunk Loses: Get one key.
Challenging Nash: Win six trophies.
Nash Loses: Get two keys.
Challenging Norm: Win nine trophies.
Norm Loses: Get three keys.
Challenging Geary: Win twelve trophies.
Geary Loses: Get four keys.
Challenging Velo: Get four keys.
Losing to Velo: Get four keys.
Defeat Velo without 100 %: Get four keys.
Defeat Velo with 100 %: Get four keys, have thirteen relics, and one Scepter.

Beat the Sapphire Relic Race time.

Once race begins, take a right. You'll see a rope holding the track together. Hit the rope and you will fall. This will take you to the 2nd jump of the track.

Finish in first place in all sixteen races in adventure mode. This includes the four Boss races as well as the twelve normal races. You will then be challenged by Velo to a race on the Hyper Spaceway track, which will now become unlocked in the other modes.

To get the CNK token letter that you see in the air during this race, after you have gone over the first bridge, find an opening between the end of the bridge and the wall. Drive into the water closest to the wall and you should end up on top. Note: Do not use this as a fast cheat because it takes a while for Aka Aka [or Uka Uka and Emperor Velo] to get you up there.

About halfway through the track you will see a piece of hanging track on the left. Go directly next to it and hold R1. Make sure your car goes on the track. This is useful in time trial mode, as there are a few boxes up there.