Part 01: Reveille
As soon as the first cutscene ends, you should see yourself climbing out of the cryotube. Thom Shephard, who is flustered, will lead you out of the cryobay, but he will be killed by an explosive door that opens. You'll notice a pair of pipes on your right if you turn around and face away from the partially opened door. Jump on top of them. Pass through two more doors and crouch beneath a half-raised blast hatch to continue forwards. Ignore the firefights in the corridor; once you have a weapon, there will be plenty of Covenant to kill, and there is nothing you can do to save these Marines and technicians. As you move to the right, you'll notice a second door on the left side of the corridor. Follow the corridor through a darkened room until you see a pair of techs and a Marine firing on some Covenant. The Marine will offer to drive you to the bridge; you can either follow him or cut around and go ahead on your own. When you reach the bridge, approach Captain Keyes near the viewport to initiate a cutscene.
Part 02: AI Constructs and Cyborgs First!
After the cutscene, Keyes will hand you a pistol. If you're playing single player, here's a tip that will help you get through this level on Legendary in one piece. Get out of the bridge as soon as you can, taking care not to collide with a wall or any of the bridge crew. If you're quick enough, your pistol will not appear when the door to the cafeteria opens. Take cover behind the nearest steel barrier with the Assault Rifle. Shoot the Grunts first because they're easier to kill and will reduce the Covenant's numbers faster. Crouch behind the barrier if you come under heavy fire. It's likely that a Marine or two has already been killed, so make sure you take their ammunition and grenades. Grab a Plasma Pistol or Rifle, as these weapons are very effective against Elite shields. Also, make sure you get some plasma grenades because they can easily kill enemies on this difficulty.
Once the room has been cleared, swap out your almost-depleted plasma weapon for a new one; there should be plenty lying around. Return to the bridge for a moment, then make a loop around the room before exiting. Your pistol will appear this time, along with a trio of Grunts. You now have three weapons to keep your chin up in any sticky situation: a rifle that can cut down a large number of unshielded enemies at once with rapid fire, a pistol that can kill enemies quickly with headshots, and a plasma weapon that can bring down shields in seconds. If you're playing cooperative, or if you haven't gotten all three weapons, I'd suggest an Assault Rifle and a plasma weapon. On this level, there will always be more ammo for them, and on Legendary, every shot counts. When your plasma weapon's ammo level falls below 30%, it's time to replace it.
Outside the cafeteria, there should be a squad of Grunts and, on rare occasions, an Elite. Take out the little guys with a UNSC weapon, and if there's an Elite, use your plasma gun to knock out his shields before switching to your human gun to finish him off. If you need extra ammo or a health kit, there's a rack with extra ammo and a health kit nearby. As you walk down the corridor to your right, you'll notice an Elite being attacked by three Marines. Go up behind him and melee him in the back if you can. If he notices you, stun him with a plasma grenade and retreat. As you exit the hall, you'll notice two more Marines guarding an airlock that will explode and kill them. Toss a couple of grenades through the open hatch, and you should be able to take out a lot of Grunts and maybe some Elites while they're still trapped in the narrow space, making the ensuing fight much less dangerous. Pick up an overshield from the boarding craft and proceed. A Grunt is standing in a darkened corridor; use your flashlight to see him. Take him out and continue on your way.
Three Marines should be fighting some Covenant from behind steel barriers. Don't go to them yet; instead, proceed to a perpendicular hallway where you can use flanking fire on them. Again, throwing some grenades into the mix will give you an advantage. When the first group has been defeated, proceed to the Marines and wait for the second group behind the barriers. When they arrive, throw more grenades and kill the survivors with whatever gun you have available. Near the next hallway, there's more ammo and another Health kit. When you see a tech killed by an explosion and smashing into a wall, move towards him and flank the Covenant once more. They're in an ideal position to avoid being hit by a plasma grenade. Once they're dead, proceed to the next airlock, where there are more overshields if yours have run out. Start with the Grunts and work your way up.
Move under another half-raised blast door when you see one. A pair of techs will be fleeing from Covenant ahead of you, but you won't be able to save them. Don't rush towards them; instead, wait for the Covenant to appear so you can take them down. There are a lot of enemies in the room, so use the lockers and benches as cover if necessary. Run to the right side and kill the Elite first if there are any left. Turn around and kill the enemies on the other end.
The next fight may be the most difficult of the mission, so make sure you have as many plasma grenades as possible and the freshest Plasma Pistol / Rifle in the area. If you only used one overshield from the previous airlock, go back and get the other one: you'll need it. If you're not at full health when you return, there's a health pack waiting for you. Then continue on your way.
Marines will eventually be seen fighting the Covenant on higher ground. Since you have your overshield, the best strategy here is to run up the stairs and try to stick the nearest Elite. If the stick fails, use your plasma weapon to deplete his shield before finishing him with your human weapon. Once that's done, try to stick the other Elite and the two Grunts, but save one or two grenades for later. Look around you to see a blast door opening, revealing Elites and Grunts inside. Approach it from either side and stick the elites and grunts in there; they won't move much. Jump down and kill the grunt and elite downstairs as soon as you finish dealing with this group and your shields are up (on the left of where you initially approached the area from).
Move upstairs and kill as many Grunts as you can. Then, hit the Elite with plasma fire before finishing him off with your human weapon. Turn on your flashlight and kill the Grunts hiding behind barrels in the next area. Try to stick the Major (purple/red) elite next. If possible, include the Minor (blue) one as well. The Grunts should be a piece of cake to deal with next.
Cortana will warn you after you pass through the final corridor that the blast doors behind you are closing. There will be three Grunts ahead of you; make quick work of them and GRAB THEIR GRENADES. Also, try to obtain the most recent Plasma PISTOL. You don't need the rifle for the next section.
Enter the tunnel and take the first left you come to. Follow the path until you reach a door. Outside, there are two Grunts. Melee the closest enemy (he's facing away) and shoot the other. Then, stick as many Elites as you can. If there are too many people crammed into the doorway space, there is another doorway to the right of this one. To ambush them, alternate between the two. When you've killed enough of them from hiding, come out and use the Plasma Pistol overcharge on the Elite shields before raining bullets or sticking them. Now, there are two Elites in the next doorway, who may or may not have been killed in the brawl.
Continue moving up until you see an Elite in the corridor opposite you. Deplete shields with plasma guns then finish of with a UNSC weapon. The Grunts are manageable, and the explosion will help you out. Enter the tunnel and melee the two Grunts you encounter; they won't fight back. You should now have the maximum number of Plasma grenades.
Continue forwards to the first exit you see and kill the Major Elite. As needed, kill the Grunts. Move into the doorway on your right (killing Grunts as needed) and continue to the right until you see a second doorway. Face the fallen locker while crouching behind it. Get up and put the elite in front of the crowd. Flank around and eliminate the Grunts. Continue moving until you're behind the grenade barrier. Continue to lob grenades (frag or plasma) and take cover until the Covenant is defeated. If any survivors remain, mop them up as needed.
Proceed to the lifeboat to start the cutscene and finish the mission.
Note: this achievement can be done on any difficulty.