Two Arbiters glitch

The Two Arbiters Glitch is a glitch that can be exploited in three Halo 3 Campaign levels: The Ark, The Covenant, and Halo. The glitch, which can only be performed in single-player, causes the Arbiter to be duplicated for a portion of the level.

The Ark
Killing the Arbiter immediately before you activate the Cartographer will result in his duplication, though one of the Arbiters will leave as scripted. The Arbiter spawned outside the building at Mission Start and Rally Point Alpha is invincible. The Arbiter spawned inside the building can be killed.

The Covenant
When you have de-activated the third tower, get in the tank before the Arbiter gets in the Phantom and blow it up while he's in it. The Arbiter won't leave the level like he's scripted to, and after the second comes down from the Phantom, it won't have a waypoint above his head. The second one may be teleported when you get to certain parts in the Citadel.

Another method simply requires that you kill the Arbiter just as Truth starts speaking, immediately before the cutscene when you enter the Citadel after defeating the two Scarabs.

Four Arbiters
The Four Arbiters Glitch is a variant of the Two Arbiters Glitch that can only be exploited on The Covenant. The glitch can only be performed at Mission Start and Rally Point Alpha.

Instructions
Pick up the Power Drain. Continue to the third tower. Destroy the Anti-Air Wraith on the left. Enter the third tower. Deactivate the third tower.

After the cutscene, escape the Flood and activate the elevator. When you get downstairs, Arbiter and the Elites will be fighting the Flood. Kill the Arbiter and go to the Flood. You will see a waypoint; this Arbiter will be carrying the Energy Sword and the Plasma Rifle. Go outside and there will be a Separatist Phantom. Destroy the Phantom. Get in the Warthog and get the two Arbiters to ride in the Warthog. Drive the Warthog to the Hornets. It is possible to drive to the Hornets without killing any enemies; any remaining enemies will be instantly killed. After you have killed the two Scarabs, the third Arbiter will spawn. Get the three Arbiters into the Citadel. After the Cortana Moment, kill the third Arbiter as you get the loading point.

After the cutscene, go to the third bridge. There will be four Arbiters. Deploy the Power Drain and headshot the three Arbiters that can be killed and activate the bridge.

After the cutscene, you will have four Arbiters that will accompany you to the end of the level. Escape the Flood.

Explanation
The glitch works on the Covenant because when the Phantom begins to engage its Active Camouflage, all of the Elites on board are removed from the level, as can be seen by players who actually get on the Phantom with the Elites. By destroying the Phantom, a player performing this glitch stops the Phantom from engaging Active Camouflage, which prevents the Arbiter and the Elites from being removed from the level. Therefore, the Arbiter remains with you. As the game is unaware of the Phantom's destruction and this Arbiter's continued existence, it spawns another Arbiter the next time the Phantom shows up.

Cloning the Arbiter by killing him prior to a cutscene is simply a manifestation of the Life After Death glitch.

Halo
By using a Spartan Laser with infinite ammo to kill the Arbiter immediately before the 343 Guilty Spark fight, players can create a "clone" of the Arbiter. Outside the Control Room, after the battle, one Arbiter will be standing around, and the other will already be attacking the awaiting Flood; the latter has the waypoint above his head. Once near the end of the hallway, both Arbiters will stay back.