Get the running shoes
After defeating new cortex, you will get the running shoes or the spring shoes. These shoes can make Crash move much faster and thus it will help you find it easier to win time trials.
Break all yellow boxes
The yellow boxes give you extra time by pausing the time. Do your best to hit all yellow boxes on your way to get a better time.
Find hidden yellow crates
The yellow boxes are sometimes well-hidden and not that visible. Know the location of these boxes to get a better time.
Finish the game first
It’s strongly recommended that you finish the game first before staring on time trials. When you get used to the levels and game dynamics, the game can become much easier.
Ignore most crates
Ignore most crates, especially the ones that would require you to waste time. Only focus on yellow creates while ignoring everything else.
Use Aku Aku
Aku Aku can be extremely helpful in time trials since you will sometimes have to get hit just to save a second or two. Whenever you see an Aku Aku box hit it for you might need it.
Jump on things
In some levels, jumping on objects, crates or enemies can help you bypass certain areas faster. This can sometimes help you get a better score. (See Why Crash Bandicoot N.sane trilogy is very difficult?)
Save the first second
Sometimes you might need to wait for a second or two at the beginning of a level for a platform to arrive. In such a case, don’t start the time trial until the right moment. This can save you a second or two.
Ignore bonus stages
If you want to win the time trial then you must ignore bonus stages. There won’t be any need for them during a trial.
Discover secret paths
Some levels have got secret paths that can help you save time. Make sure you find those paths to increase your chance of winning. (See How To Win Final Fantasy 9 Card Game)
How to Win Time Trials in Crash Bandicoot 2 (PS4)
Crash Bandicoot 2: Cortex Strikes Back – How to win the Time-Trials guide