There are a total of 8 terminals that can be found in Halo 3. In order for the achievement to unlock, you must cycle through the dialogue and wait until the terminal is done changing. The terminals are as follows:
[
0:09] - Terminal 1 - Mission: The Ark
[
0:31] - Terminal 2 - Mission: The Ark
[
0:54] - Terminal 3 - Mission: The Ark
[
1:21] - Terminal 4 - Mission: The Covenant
[
1:49] - Terminal 5 - Mission: The Covenant
[
2:39] - Terminal 6 - Mission: The Covenant
[
3:18] - Cortana’s Terminal - Mission: Cortana
[
3:47] - Terminal 7 - Mission: Halo
Collecting all 8 terminals will also unlock the following achievements: