Easy Achievements
To complete the easiest achievements available online in Halo 3, simply playing the game for an extended amount of time will do the trick. The "Graduate" achievement is rewarded to players who complete 10 online games in any mode (win or lose) or gain five EXP, whichever comes first. For the "UNSC Spartan" achievement, gain EXP by playing matches until you are promoted to sergeant. Likewise, the "Spartan Officer" achievement is rewarded upon promotion to officer.
Two For One
For the achievement "Two for One," you must kill two enemies at the same time using the Spartan Laser. This weapon is extremely powerful, but it takes a long time to charge before you're able to fire it. To get this achievement, plan ahead. Hold down the trigger button to charge the laser, then release it right before you fire. Keep doing this to keep it charged. That way, when you have two enemies in your sight, you can fire a shot off almost instantly.
Banshee Attack
To complete the "Too Close to the Sun," take down an enemy banshee vehicle using either the Spartan Laser or the rocket launcher. Since the rocket launcher has a faster rate of fire, it's a safer bet against a moving target like a banshee. However, it does not lock onto enemies, so you must aim manually. To give yourself a better shot, tag it with a charged blast from a plasma pistol to stall the engine, then switch to your rocket launcher and fire.
Headshot Honcho
Earn the "Headshot Honcho" achievement by getting 10 head shots in a ranked free-for-all match. There are a number of strategies here, but the most practical is a compromise between medium and long distance. For close-quarters combat at medium range, the most effective weapon is the battle riffle. Three quick shots to the body will deplete an enemy's shields, then one head shot will drop them as they retreat for cover. In levels over long, open distances, select the sniper riffle. Target a highly trafficked area with your scope and fire one shot to the head to take down an enemy.