Pretty straightforward. Keep the sniper handy until the Banshee fights. On the beam, you want to snipe the Brutes as you are walking. They can throw Bubble Shields.
You will need to shoot down the Phantoms to progress the fight faster along with the Banshees. The Phantoms that deploy enemies don't get shot down. There are Missile Pods littered around the Pelican and two that are mounted. Only take them off once the Phantoms that come out from the same side are eliminated. Phantoms have three spawn points and randomly spawn each time the level is played. Banshees also assist the Phantoms and the Spartan laser will come in handy if one is too far out for the Missile Pod. The Spartan Laser is useless against Phantoms, but six shots from the Missile Pod will work when hit at one of their 'eyes'. Once the three sets of Phantoms are destroyed, one last Phantom flies from the bottom, take a Missile Pod and shoot it 2-4 times. Once it has set up its spot, rocket the eyes and Buck should say "Jet packs!". If he doesn't and the Phantom is destroyed, the game softlocks. Head up top to end the level.