From Halopedia, the Halo wiki
The Quad Shot is a button combo for Halo 2.
The Quad Shot's button combo is: R, R, X, Y, Y, R, R, X
It is a more difficult but more powerful version of the popular Double Shot, who's button combination is R, R, X.
Quickly press and release R. As soon as you release it, quickly squeeze it again- but this time, hold it down. As SOON as you hold it down, follow these directions quickly. Press X- this is in order to have the two shots burst out at the same time, or rapidly following each other. Timing is crucial, as there is about 1/10th of a second to do so, and within that small window, the pace, or rate of the shots is also determined. Next, you want to cancel the reloading (by pressing Y twice, in quick succession), and do the Double Shot again. This also happens to work for the Halo 2 Vista game.