Halo 4

This achievement requires you to find all 7 terminals in the game.
Once you find them you need to press the action button to download them. Once downloaded they will be uploaded to waypoint where you can watch them .

Terminal1
Mission 2 : Requiem
Unlocks: Terminal 1: War
Load up Rally point Bravo. Then blast your way through the mission untill you see two hunters at the end. Kill the hunters and proceed through the door. You will come to a long hallway and will see an orange ramp ahead. Below the orange ramp will be the terminal.

Terminal 2
Mission 3 : Forerunner
Unlocks: Terminal 2: Lord of Admirals
Load up rally point Bravo. Make your way through the mission until you get to a large circular platform. It will be a couple minutes into the mission. You will see a knight and crawlers all around the rocks. Kill them and wait. Your HUD will be distorted and cortana will say it was because of her, when this happens you will see the terminal at the bottom of the forerunner structure.

Terminal 3
Mission 4 : Infinity
Unlocks: Terminal 3: Charum Hakkor
Load up rally point Bravo and its directly behind you. If you're getting all the terminals on your first playthrough here is what to do. Once Lasky tells you to clear an LZ and Cortana mentions a space in some foliage turn around and it will be there.

Terminal 4
Mission 5 : Reclaimer
Unlocks: Terminal 4: Flood
Load up rally point Bravo. After you pick up Cortana and kill all the enemies in the room, there will be a door all the way ate the back. behind the door is a hallway to the left and right and an elevator in front of you. Take the hallway to the right and you will see the terminal.

Terminal 5
Mission 6 : Shutdown
Unlocks: Terminal 5: Knights
Load up rally point Delta. When Cortana marks the objective on you HUD go to the left structure instead. Behind the pillar is the terminal. IF your going for all the terminals on your first playthrough then it will be in the third landing zone when flying the pelican.

Terminal 6
Mission 7 : Composer
Unlocks: Terminal 6: Justice
Load up rally point Bravo. After meeting up with Dr. Tilson go outside and you will see the word 'Atrium' written up on the right on a wall. Below the word 'Atrium' will be a cave with the terminal.

Terminal 7
Mission 8 : Midnight
Unlocks: Terminal 7: Cryptum
Load up rally point bravo. The terminal is located in the third room. In this room will be a pillar in the centre, behind the pillar is the terminal. You will get into these rooms after the flying sequence.

Credit to Youtuber: ToiletGamers for the following video.

The video linked will be available when the game releases on November 6th, 2012. Also, I have provided a text guide that shows all the terminal locations:

Requiem
Shortly after defeating the first two Hunters, go inside the building and check underneath the main ramp.

Forerunner
After your HUD starts to flicker and Cortana says it's because of her, it's at the base of a Forerunner structure. This is just after Rally Point Bravo after defeating a set of Prometheans

Infinity
After meeting up with fellow USMC soldiers, following a cutscene with Lasky, turn around before running outside and the terminal is directly behind you.

Reclaimer
Near the very end of the level, you will pick up Cortana and trigger a long cutscene. After the cutscene, fight the Prometheans that spawn and then continue through the first set of doors. DO NOT GO UP THE ELEVATOR. The terminal is on the right just before the elevator.

Shutdown
At Rally Point Delta, on your way to the checkpoint where there is an elite with a fuel rod cannon and two hunters, go to the structure to the left of the waypoint, and the terminal is behind the spire.

Composer
After killing the hunters and then going outside after a cutscene, look for the word "Atrium" written big up on a wall on the right. The terminal is located in some caves below the word Atrium.

Midnight
After the flying sequence is over, you'll fight your way through some large Promethean hallways. In the 3rd room, look behind the central structure for the final terminal.

There are 7 total terminal locations, and you must access them (using x - by default) to unlock this achievement. There will be spoilers in the video and text description. View below:


Location 1: Requiem [0:06]
At the end of the level, after defeating 2 hunters, you will come to a long hall. At the end of the hall you will view this terminal in plain sight under a clear ramp that leads to the end.

Location 2: Forerunner [0:35]
After a few minutes, you will defeat a small group of crawlers and a promethean, and your HUD will begin to become distorted. Once this happens, the terminal should be in a relatively plain sight under the tower structure.

Location 3: Infinity [1:05]
After meeting up with your teammates, there will be a short cutscene and you will spawn inside a ship. Just turn around and the terminal will be directly behind you.

Location 4: Reclaimer [1:28]
Midway through the level, after the first main cutscene, you will end up indoors. You will have to pick up Cortana and make your way through a hallway. Instead of boarding the elevator (primary on-screen objective) take a right and the terminal should be there.

Location 5: Shutdown [1:55]
When progressing through this mission, you will come to a section with a bunch of light bridges. At one point you will reach the end of the path and two hunters will appear. The terminal is directly before this checkpoint, but you can easily backtrack. When going from the entrance to the location of the hunters, take the last possible left and the terminal will be located behind the structure on this platform.

Location 6: Composer [2:21]
Once you reach the outdoor part of this level, run across the terrain to the building that says "Atrium" on the side. At the base of that sign is the Terminal. The "Atrium" sign does repeat itself on the side of the building, but this is one the closest and in the most clear sight from where you begin this section.

Location 7: Midnight [2:59]
Once you get to the part of the level where you are in foot, progress through the story by clearing the rooms of enemies and moving forward. Once you enter the 3rd or 4th room, you should see the terminal located behind two pillars. Walk around to the back side to access it.

Welcome everyone to our video showing all locations of the terminals! I would have loved to have risked uploading videos like others early. But i would like to keep my relationship with Microsoft intact

Enjoy!

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Mission 2 Terminal 1 00:00
Mission 3 Terminal 2 00:45
Mission 4 Terminal 3 01:11
Mission 5 Terminal 4 01:40
Mission 6 Terminal 5 02:05
Mission 7 Terminal 6 02:43
Mission 8 Terminal 7 03:15