To start with, most of the Time Trials in later Hot Wheels City are impossible to beat by just simply racing the track. This means that you are required to find and use shortcuts to beat the clock, often by abandoning the notion of racing along the standard rout.
For most of the time trials, it is helpful to use fast vehicles (maxed speed and acceleration, such as a legendary level 24 Ours car) that have 2 or more boosts, or a vehicle with a medium/large boost tank. That way you will have the speed and the boosts to jump the track.
The next key skill is using air controls. Most shortcuts involve flying off the track and going off road, meaning that you will often have to deal with your car not landing smoothly. By getting a handle on air controls, you can prevent yourself from wiping out while taking shortcuts and shave off valuable seconds.
A final skill needed is drifting. It may be obvious but some shortcuts involve precise drifting to clip the edges of checkpoints.
A very helpful place for shortcut guides are by TwinDrags [F1JD] and DDragonShark on YouTube. (Note that I am not the creator of the videos so please show support to the creator!)
(I also added my general thoughts on the difficulty of the track after taking the shortcuts)
(Note, these shortcuts still work after the November 3rd checkpoint changes update!)

I recently discovered that on non-turbo starting lines (that is, not the ones where you have to spam boost) if you get a boost, then stop accelerating (losing the boost) you will start the time trial with a full boost bar/dots. That is to say, you can start a race with more than just 3 boost charges, making some tracks just a bit easier. Similarly, just waiting to passively gain full boost by waiting behind the starting line would work just as well.

Secret Treasure Hunt cars (STH) are extremely rare cars found by opening crates (it took me nearly 200 crates to get my first STH car). However, if you have around 2000 credits and a lot of time, you can buy them from the limited offers shop. the STH cars will be towards the end of the shop. for STH versions of existing cars, the cost will be identical to the cost of the normal variant.
The are rare chance appearnaces in the limited offers page and are not guaranteed to always be there. If you preview the car you can see if it is the original or a STH variant.

I do not have all the shortcuts shown in these posts, some may or may not be needed to be used. I am aware of some easier shortcuts for some levels exist and would appreciate any feedback or assistance in acquiring videos or images to be used to help fill in the guide. Feel free to add the information in the comments and I will do my best to add them into the sections of the guide!

Slam Race:(easy)
This race is pretty straightforward, just have a clean lap and hit the boost pads and you will beat it easily.

Snake on an air duct: (easy)
The main shortcut through the vents and the off road shortcut are very easy to do (the off road shortcut can be used to land further back on the turns to make the landing easier). Overall, use a car with two or more boosts and you will be all good.

Wind Tunnel:(medium/very easy)
To beat this level, you will either need the perfect run, or to take the second shortcut shown (the one where you drive backwards to get to the checkpoint before the forced re-spawn). By taking only the second shortcut, and having a fairly clean run, you can get just under the unleashed goal time.

[Update!] Alternatively, I have found an easier shortcut. Race like normal until you see the first tunnel (picture 1). Veer off the edge aiming for the blue track bend below (picture 2). Land on the blue track below and drive (picture 3). If you miss, just reset and try again, the shortcut cuts out around 30% of the track, meaning if you do this one shortcut, you can easily beat the time trial.
This can be done with any car, the only challenge is landing on the blue track below and driving to trigger the re-spawn point below.

Jurassic Skate Park: (very challenging)
For this track, you can ignore the first shown shortcut and just race normally. Once you reach the second shortcut, follow the rout shown in the video. This will be really difficult to beat the unleashed goal time if you wipe out or reset. Even with a perfect run using the rout shown, I barely made it in time.

Dangerous Perspectives:(easy/medium)
This race, there is no need for shortcutting, but it could be helpful. I would recommend just trial and error for this particular track, with the spiders being the main challenge. (You can "juke" spiders by either suddenly boosting or by suddenly changing direction, causing the webs to miss your car). Honestly, once the spider web rng is dealt with the rest is just clean driving.

Stunt Parking:(hard)
This track can be beaten under time if you can take your corners just right. The video's second shortcut (the off road U-turn) is the only thing that you must get down if you want to beat the trial. (The flying section is optional and would be a significant help in beating the time trial if you can get it down)

Garage Yo-Yo:(medium)
This race requires the use of the first shortcut (the dropping off of the magnet track). After taking the first shortcut, just have a clean race (save 2 boosts for the 2nd and 3rd loops) and to not reset. The hardest part of this race is nailing the landing on the shortcut, as this will make or break your run.

Wild Wild Skates:(medium/hard)
The only shortcut needed for this track is the off-roading done to reach the first 3 checkpoints. After that, you can just race the track. The challenge for this track is that the first 3 checkpoints are very picky and don't always get triggered even when you hear "Checkpoint" being said. You must make sure to pass through these checkpoints cleanly to get the most out of the shortcuts and to create a larger surplus of time to offset any mistakes made on your lap.

Bridge Overtakes:(very hard)
You will need to take all but the final shortcut shown to beat the time, the reason being that the final shortcut can wipe you out and destroy your run. This course will require you to fly your car up to the top section of the first splitting bridge piece by tilting your car back with your air control keys and then boosting. Of note is that ONLY the left side of the second splitting bridge piece will allow you to reach the checkpoint.

Volcano Project:(medium)
For this track, take all the shortcuts shown in the video. The first shortcut saves a significant amount of time, so you can take multiple attempts at doing it before having to restart the race.

Applied Gravity:(very easy)
This track is impossible to beat without taking the shortcut, trust me on that (I spent over 5 hours just trying to beat the 1:20:00 time...). This shortcut is really simple and shaves off more than enough time for you to beat the time even without a maxed out car.

Vertigo:(easy)
For this track, you don't have to take any shortcuts. You do need to have your drifts on point and make use of your boosts.

Magnetic Fields:(easy)
Again, this track won't require any shortcuts, although the second shortcut shown may be useful in beating the trail if you are having troubles with this course.

Gas Gas Gas: (medium)
This track, as the name implies, is all about flooring it. To beat this track, just simply race it and avoid wipeouts and the spiders. A trick for the wall-less U turn section is to grind against the wall to slightly slow down and thus get the drifting right.

(Sorry no shortcut video here, as there are no shortcuts)

Speed Vault: (easy/hard)
This track is the first time trial unlocked, however, it will also be one of the latter time trials to beat the ultimate goal on. The real challenge is not the track, but rather the speed of your car. To easily beat this track you need a flawless run and a maxed out car, something that is unlikely to be unlocked in your starting 3 crates. As such, you need to do races and other time trials to upgrade cars and to open boxes, then return to crush the track!

(Again, no videos, as there are no shortcuts)

The tracks in the video are in numerical order in Hot Wheels city, not by order of appearance.
Please note: it is virtually impossible to beat the time trials without using shortcuts!!!!!

From 0:09-2:01
Where's the Suit?: (hard)
This track requires the first and second shortcuts, though the third shortcut is not needed. For this track, you need to have a car with 4 dot boosts and high speed.

2:02-3:35
Hangar Tour: (medium/hard)
This track requires the use of the shortcut. The real challenge is dodging the spiders and having a clean run.

3:42-4:52
Jokers Playground:(easy)
This track requires use of the first shortcut and at lease one of the other two shortcuts. Only difficulty is landing the first shortcut and avoiding the hammers.

5:00-6:44
I'm the Night: (very hard)
You must take the shown shortcut and have a flawless run.

6:52-9:30
The Last Laugh:(very hard)
You need to preform the first, second, and fourth shortcuts and use a car with at least 3 boost dots. This is likely one of the hardest time trials currently in the game!

Thanks to DDragonShark for allowing me to use his video!!!!

As of current, there are not many time trial videos. Instead, I have been allowed by DDragonShark to share his video on some of the currently known shortcuts for the new tracks. These difficulties are ranked by DDragonShark and I do think that they are accurate to the overall challenge of each shortcut.

Warning: these tracks are exceptionally difficult. You may need to grind to beat these. After the massive shortcuts found on Batman and regular stages, the devs tried to limit the shortcuting of the tracks, but forgot to reduce the time to reasonable time frame. Beware the off road sections of the track, they can easily tank a perfect run. Similarly, the swinging ball track piece is spammed a lot in the tracks, and it has a larger hit box than the ball itself.

This video is courtesy of DDragonShark, thank you for letting me use your videos for my guide!!! This is a list of shortcuts for the new tracks.

Warning: these tracks are heavily shortcut resistant. Instead, grab your fastest car with the most boosts and drift and boost appropriately. These tracks are all about speed, so any car that doesn't have max speed will be nearly impossible to get the time you need.

Again, please show support to the Video Creators, all I have done is just made them available here for easy access.
P.S. This is my first guide, so please excuse the roughness of it :)