How do I move super quickly?

You Homing Boost

The video above is old but its basically what you need to learn

Homing Dash is the main unique mechanic which seperates AH3 from other Fighters. It is a dash which will ignore gravity and pull you towards the opponent.

In AH3, this homing dash cannot be stopped without attacking in some way. If you stop the homing dash with an attack, you will no longer be pulled towards the opponent and instead just fly in the direction you were going in when you attacked. However, you should notice that you are moving a lot slower than in the match videos you may of watched

This is Clarice, she is super fast

As you can see, she traverses the whole entire stage in maybe 0.5 seconds. Probably less

This is due to a mechanic in AH3 called Homing Boost. If you press D again plus a direction while in Homing state, you will gain a speed boost in that direction. This speed boost is lost quickly and eventually you will go back to normal speed. Now if you try this, you probably still don’t get the same speed

D -> D again = Homing Boost

Now, there's is a technique I call Homing Boost Cancel, others call it Speed Homing. In Japan I have no clue what they call it. Homing Boost Cancel allows you to boost with an attack and retain almost all of the speed gain from Homing Boosting, without the speed dropping off over time.

You essentially just Boost and attack as soon as you can so you don't lose any speed.

The inputs are

Start a Homing Dash. j5D moves the fastest and is very noticable when you HBC correctly, so its recommended you use j5D to start with
You then hold a direction you want to bend towards
jD to boost, then immediately press an attack button

If you do this correctly, you should fly at a very high speed, with a button flying out. The best way to check if you have gotten the input correctly, is to actually do D~A. If you use A, you SHOULD get a throw since D+A is throw. If you do not, you are either amazing and you have managed to let go of D before hitting A, or you are doing it too slow.

jD -> D~X = Homing Boost Cancel

The best way to practise this in my opinion is to

Pick Clarice
Reset the stage
Instant Airdash backwards
Press j5D
Homing Boost with 8D instead of just D
Plink/Piano into A while holding up

If it is done correctly, it should look like this

You will zoom past the opponent, while doing an Air Throw. Air Throw recovers so quickly, that you can even start ANOTHER Homing Dash, and get another HCB to return to the original spot.

This is all you need to get the basic Homing Boost Cancel / Speed Homing down. One thing to remember is that, you may be doing Homing Boost Correctly, but every character has different Boost Speeds, Clarice being by far the fastest

I also recommend checking the video above, so you can see the timings and some usage points of Homing Boost

Pick Clarice and try to do the above practise routine
Set the opponent to jump and try the same thing, notice how the position of the opponent changed the Homing effect?
Practise at different distances
Try it with your main Character