Hangar Bay: 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.