Chances are, you are going for completing all Halo 3 missions in under 3 hours on legendary, and if so, you will unlock this achievement along the way. If you are, then refer to youtube videos such as those made by "Halo Completionist", "Nak3d Eli", or speed runners on youtube. Another great option is to play in 4 player co-op on legendary. If your team is decent at all, you will easily complete the game on legendary and you have a great chance at completing the game in under 3 hours, unlocking this achievement, "Devastating", and most or all of the par time achievements.
If you do not care about any par time or speedrun achievements and you just want to complete all Halo 3 missions on legendary, then you can play coop with one other friend who is willing to be a spawn point for you (or you can be the spawn point for them) as you grind your way through the missions. It will take longer, but as long as one player stays alive at all times, you will make it through the game. If you have a second controller or have a partner who has a second controller, then you can either do this "solo" in coop by using a second controller as a spawn dummy or in coop with a friend so that both of you can play while one of you uses a second controller for both of you to spawn on when you die.
If you play by yourself using two controllers though, be aware that the mission "Cortana" (second to last mission) can sometimes be frustrating because if you die on your main controller, your dummy could be "in combat" which prevents you from spawning or your dummy controller could be attacked later in the mission which means if you die, you have to revert to last checkpoint.