Terminal 2 - Mission 3 'Forerunner' - Rally Point Bravo
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.
Terminal 4 - Mission 5 'Reclaimer' - Rally Point Bravo
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.
Terminal 5 - Mission 6 'Shutdown' - Rally Point Delta
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.
Terminal 6 - Mission 7 'Composer' - Rally Point Bravo
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.
Terminal 7 - Mission 8 'Midnight' - Rally Point Bravo
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.