There was 2 battles: Space and Ground. Space was Captain Keys vs 3 Covenant ships. After discovering the Covenant were fighting unusually in space he investigated with his scanners and discovered the main ship was deploying drop ships. Keys success fully defeated the 3 ship using what other members in the fleet called the "Keys" Maneuver. After this reinforcements arrived. The second part of this space battle was multiple UNSC ships vs multiple covenant ships. Skipping to ground operations: Master cheif along with his fellow Spartans were assigned to deploy a HAVOC nuke in Cote D' Avur (something like that) John achieved by first going through a jungle, then arrived at the major city, while moving about discovered the race Engineers and Hunters. They then acquired a strange object that was gem-like in appearance, later nuke was successfully detonated.
Outcome: covenant was defeated and UNSC had defended a planet from being glassed. The information from the gem suggested other alien race (forerunner), also during the battle a small covenant probe attached to Keys ship, which led to the discover of reach and the fall of it.
I think that was pretty much it, I skipped some details because that would be too much text
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Correct! You actually gave more detail than I was looking for, since I only wanted the space bit. But the more the merrier.