Advanced Air Tricks are the tricks that require three button presses before a jump. Every possible combination of button presses adds up to 24 tricks - load up a Free Surf game (I suggest Australia for its relative ease) and go down the list one after the other.
You can build up your Surf Meter faster by holding RT and rapidly wiggling your left stick side-to-side.
Here's a list of combinations for use as reference:
X A B
X B A
X A Y
X Y A
X B Y
X Y B
------
A X B
A B X
A X Y
A Y X
A B Y
A Y B
------
B X A
B A X
B X Y
B Y X
B A Y
B Y A
------
Y X A
Y A X
Y X B
Y B X
Y A B
Y B A