The Truth and Reconciliation
Halo Runs record page: http://www.haloruns.com/records?lb=103 (click the timestamps for video links)
Outside the ship
Once you land, turn on your sniper night vision and flash light, then go to the first area with enemies.
Do NOT use frags until the grav-lift fight! On easy, none of these enemies will do enough damage to kill you, so try to keep running in a straight line towards the next area at all times. Snipe the elites coming around the corner, and AR any grunts ahead of you, but don't kill anything not in your way. Ignore enemies in the next area, jump on the slanted rock next to the health pack, snipe the elite on the path in front of you, and continue through. AR the grunts ahead, then take a hard right and crouch jump onto the rock. Once you're on the rock, wait a second to stop any momentum you might have, then crouch jump onto the ledge. Walk as straight as you can through the rocks to the next area. Shoot a little bit before you enter the path with the two elites. Once you see them, snipe them, making sure to only use one shot on each. If you have less than 2 sniper shots left, reload before moving on.
Once you've gotten to the last outside area, the gravlift, you should be killing enemies as fast as possible. As you come into the area, wait just 3-4 seconds, then look up and shoot the elite on the ledge, followed by the grunt in the turrent if he spawned there(you can kill grunts in turrents with the sniper just by sniping the seat of the turrent). If he didn't, don't worry about it yet. You need to go into the open area, and kill the elite, 5 grunts, and the 2 jackals to trigger the next spawn. Count out loud if you need while AR-ing the grunts and the jackals on the ground. If the turrent didn't spawn in the start, shoot one of the three around the area. If you killed everything, you should hear the Cortana dialogue about a covenant dropship inbound. If you do, kill the remaining 2 turrents, and stand on the edge of the grav-lift. Shoot at least three of the four grunts out of the ship as they come out to start the grav-lift fight. Try to kill all 4, as it will make the next part MUCH easier.
The moment the grunts are dead, switch to AR and throw a frag onto the center of the grav-lift. Shoot your AR a little bit to make them come down a little faster, then shoot the elite. This is where killing all grunts comes in handy, each wave spawns when there is one enemy left in the area, and the jackals and grunts like to dodge the frag. Pay attention and make sure everything dies if you only killed three grunts, or one survivor if you killed them all. There are four waves, do the same for each wave as you did the first. Once all four waves are dead, grab a plasma pistol, frags, and health if needed and go to the edge of the lift closest to the health.
This trick comes in multiple parts, including the wraith teleport, upwarp, and platforming. Here is Garish's tutorial on how to do it.
To get inside the wraith, you have to crouch next to the right wing of the wraith as it blows up. To set this up, on Easy, throw two grenades (two frags or a plasma then a frag), and shoot 6 plasma pistol shots. On Legendary, throw six grenades, or 5 grenades and use a plasma pistol to lower the wraith's health.
Once the wraith blows up, you should be inside the wing, then aim slightly to the right and move left. If done correctly, you will be inside the wraith in a corner. From here, look at the corner geometry in the ground, and lightly tap right for a one-tick input, then look straight down. You should be looking at the tip of one of the patterns on the ground. If done quickly enough, you can get a checkpoint here before the upwarp.
To get out of bounds on the top of the level, hold space and move backwards. If you do not fly upwards with a lot of speed, adjust your reticle's position very slightly to the left or right. Then, you can either land on the pillar to the right by looking towards it and immediately holding forward or forward and right, or on the very small ledge by moving slightly forwards and right.
On legendary, once you land, kill a marine so you only have to kill one in the prison section.
There are multiple ways to do this platforming section. At the start, walk down to the door which is next to the camo and health pack and land on the top of the wall. Then look towards the belly room which is the only visible part of the level. Jump backwards once and walk backwards and right until you reach a corner. Then look slightly to the left and hold jump and left until you reach a wall, turn slightly back to the right and jump to the left twice until you reach another corner. Then jump back and left very slightly.
On easy, you can skip the rest of the platforming by jumping back and right at this point and proceed through RNG room. Or you can continue doing the platforming past it.
From here, walk backwards while look slightly left until you reach a corner, then look at the left corner room and jump back once, walk back for a split second and jump backwards again. Then look to the right while still moving backwards until you reach another corner. At this point, you want to look at another corner on the right side of the room which forms an 'L' shape. Here you want to strafe jump right by moving right first then immediately jumping then once your reticle passes the bottom section of the L, hold left until you reach the last corner. The look at the center of the room at the center of a pillar and hold jump and backwards until you land back in the room.
A time saver used in all Truth and Reconciliation runs occurs in this hangar bay. While there are three possibly ways to advance to the third level, the method explained below is the most reliable and, on higher difficulties, might even leave you with a little bit of overshield left.
Head over to where the overshield is and perform a grenade jump up to the second (or if you get really lucky the third) level of the hangar bay as shown in the video. A recommended set up is three plasma grenades + 1 frag grenade. If you have less than three plasma grenades where entering the hangar bay, take some time to kill some grunts/elites until you have enough. After landing on the second level, head to the middle of the room where an elite is shooting down onto the floor level. Kill him (optional but recommended on higher difficulties) and set up for a regular jump onto the covenant ship using a box to land on a holographic projector structure in order to jump onto the ship. Then perform a grenade jump neat the rear of the ship to jump to the third level.
Skip Blob Room Dialogue
After releasing the marines from the prison, head back to the room where you faced a gold elite and other enemies. Just before the long hallway right before the room, stop and kill two marines (not Keyes) and all the marines will turn hostile towards you. Quickly head to the room and kill the two or three (depending on difficulty) invisible sword elites. As soon as the last elite dies, the level will end, skipping roughly 20-30 seconds of dialogue (this is assuming the hangar bay skip was performed). Be sure to skip the end of level cutscene as early as possible, otherwise pressing A will just revert back to a point in the cutscene and you will need to manually watch the entire cutscene to progress to the next level.