On this mission there isn't any Terminals, but there is an interactive panel under Master Chief's cryo pod which you can activate for the "Digging up the Past" Achievement.
Go out of the cryo room and look right. Jump down and look under the stairs.

Spawn at Rally Point Bravo, Shortly after defeating the first two Hunters, go inside the building and head down the long hallway. Before going up the ramp and onto the elevator, check underneath the main ramp for this terminal. It resembles a large column with a small glowing spot on the front.
Where it is
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Spawn at Rally Point Alpha, At one point soon after the first few waves of enemies in the level, you experience distortion from your helmet visor. Cortana contacts you about causing the distortion. After this exchange, a rocky ramp leads upwards into a Forerunner spire. At the very base of this spire is a hard-to-miss Terminal.
Where you should be at
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Where it is
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Spawn at Rally Point Bravo, Halfway through the level you will finally come across the UNSC forces from the downed Infinity. After the cutscene with these marines, turn around and access this Terminal inside their Forerunner structure holdout before heading back into the jungle. Really hard to miss!
How Bravo Starts
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Turn Around and look
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Spawn at Rally Point Bravo, After you talk to the Librarian and get Cortana back, you'll face a room full of Knights and Crawlers. Go through the door at the end of this room and turn right in the hallway to find this Terminal. Do this BEFORE getting on the elevator!
Don't Go On This! Turn Right!
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Here It Is
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Spawn at Rally Point Delta, This Terminal is in the third and final tower you pilot the Pelican to. Upon entering the tower you will take an elevator up to an area Didact is transforming. The path through the area leads across several light bridges, but the path forks at one tower in three directions. Take the fork that leads to a dead end with this terminal on the rear side of the tower. Note that the fork in the direction of the waypoint will take you to the platform with an Elite wielding a Fuel Rod Cannon.
No Hunters
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Go To the Right
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Back Side
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Spawn at Rally Point Bravo, When you are on the asteroid with the artifact, you will be directed to a door across the way on a platform with a single Mantis. Before going inside the airlock door, follow a tube-like passageway beneath the platform to find this Terminal embedded in the asteroid's rocky core.
Go This Way
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Go Straight for this
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Here It Is
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Spawn at Rally Point Bravo, Once you touch down on the Didact ship, you will enter a series of hallways with Watchers and Knights. When you first here Didact speak about stopping you by force, you will make a U turn through the passages with the first few enemies. In the U is a glowing blue set of spires. A terminal is nestled among them. This is right before Cortana advises you to turn left.
Behind This Pillar
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Here It Is
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