Similar to the Fission Metroids, Metroid Prime will change colors on parts of its exoskeleton. This will help you determine what beam weapon you have to equip. Instead of using just your beams, however, it's best to use the Missile Combo upgrade if you have it:
Yellow = Super Missile
Purple = Wavebuster
White = Ice Spreader
Red = Flamethrower
If you run out of Missiles, just fall back on your Beams. The battle will last throughout four individual subchambers. In the first subchamber, Prime will only switch between Yellow and Purple. Subchamber 2 is Yellow, Purple, and White; Subchambers 3 and 4 are all four colors, but in Subchamber 4, it switches more quickly and less predictably.
Each chamber has grooves along the bottom. These are for you to Boost Ball through when Metroid Prime rears up to charge at you. After you make it to the other side, immediately unmorph and attack it.
Prime will also shoot glowing orbs of different colors that will home in on you. These hurt quite a bit, so try your best to avoid them. You can shoot them with a color-coded charged beam blast before they even get close, so be on the lookout for them at all times. If you destroy them, they usually drop health, so use that to your advantage. Prime will also shoot concentrated beams at you as well as a homing attack that drags you in closer to it. You can easily avoid these, but if you get caught in the homing attack, blast it in the face a few times, and it will let go.
It may take you a few tries to get the patterns down, but after you do, get ready for Prime's final, true form. Good luck!