Final Rush is the last action stage of Hero story. It is very technical and is for huge parts made up of rails, which are the fastest form of movement in the stage. So if possible, you should stay on rails as much as possible. Most of the stage can be skipped.
Level start to first checkpoint
Don't hold forward when you drop down from the rocket at the beginning, until you're about to land on the rail. Once on the rail, do a short jump and bounce back onto the rail, this will accelerate you faster than just sliding down. Be careful, if you do it too quickly, you might drop through the rail and die.
At the end of the rail is a trick ramp, but don't actually use it. Jump over it and bounce accelerate onto the platform below. You charge a spindash on the platform, roll off it without jumping, and bounce onto the rail that starts right at the end of the platform and goes down. At the end of this rail, hold slightly up right, to drop from that rail right on the next rail that goes in a S-turn down, around a floating artifical chaos.
This rails goes directly over to another platform. This platform has a line of rings on it, so hold B while you're still on the rail in order to charge a spindash on the platform without accidently activating a light dash. You spindash off the platform and go slightly to the left, to bounce onto a rail that starts after the platform you spindashed off and goes off the the left, but then quickly goes in a S-like shape down around a square platform and then forward again.
As this rail continues, it has a short cut in it as it does down steeper and the back up again into the tunnel. To avoid flying off at that cut and losing lots of momentum, do a small jump at the end of the rail and bounce back on it as it continues. This rail brings you to the first checkpoint.
From the first checkpoint you bounce onto the rail further down the goes off to the right, into the huge blue tower where it spirals down. From this rail you can continue the stage normally or do the level skip.
The idea behind the skip is to bend gravity to the side and move very far out to go all the way around a killplane. From there, you reset gravity, turn around and fall towards the goal ring.
The variation explained here is the bounce variation. It can also be done bounceless.
The rail that goes to the right into the tower has just as it goes to the right a very steep part. This is the part you want to use to bend gravity to the side. You jump off from that part of the rail, and a short moment later you bounce. Then you want to hold the left camera trigger and turn around, until you're holding an up-left angle on your control stick. You now should see Sonic bounce diagonally. Make sure Sonic's angle is at around 50°+ (a bit higher than 45°), and hold that direction. You need to hold the angle for around 18 seconds from jumping off the rail. So when you jump off, look at the timer and add 18 on, then you know for how long you need to be falling diagonally. It is recommended to experiment a bit with the angle and the timing for the left turn, because it is very important to get a feeling for what to do. If you turn too early, you might hit the killplane and die, if you turn too late, you might not get enough height to make it to the goal ring.
When the 18 seconds are over, move your control stick up in order to reset gravity back to normal, then turn to the left. To get towards the goal ring, you can use the background texture of the earth as a reference point. On the earth you will see a round shape of clouds, sort of like a bay. If you adjust your direction until Sonic is above that point, you are falling towards the goal ring. Make sure to fold forward at all times.
After a while of falling forward, you should see the ending of the level appear in front of you as 3 huge inverted towers. There is a killplane between you and the goal ring. You can dodge it by placing Sonic to the right of the middle tower and moving around it towards the goal ring. If you notice you are going low on height, you still can homing attack cancel once to get extra distance.
From the direction youre coming from when doing the skip, there is also an invisible wall around the goal ring if you're low on height. It is shaped in a way that it's supposed to push you away from the goal ring, but you can push against it and make it savely onto the platform with some practise.