The Elephant Rush is an all in early game rush for use with Captain Cutter and the UNSC. You start out building an Elephant and a Supply Pad as you send your first Warthog to grab supply crates. Build 2 more supply pads as you get the resources. As soon as your Elephant finishes send it to setup at the enemy base (use the 'Y' button). Build another warthog and keep gathering supply crates.
Build a Reactor as soon as you can (after you have 3 supply pads). By this time your Elephant should already be in the enemy base producing units. Usually what you want to build are Flamethrower squads, especially if it is against the Covenenat, because they're excellant against grounds units (remember to set your rally point next to the enemy base unit exit). You also can build more Warthogs if you have the resources to do so. You mostly want to gather supply crates with them but you can also use the to run over enemy units, just be careful not to lose any hogs. If any get low on hitpoints send them off to gather more supply crates. Be sure to target any enemy units that come out, and kill turrets before they finish building.
After your Reactor finishes build Spartans and research Gunner for the Warthogs then keep building Supply Pads. By this time it should be a winning battle for you at the enemy base. Look at the buildings your enemy has and decide what to do from there. If he has a Factory or Summit build more warthogs and make sure you get 3 spartans then get marines. If he has a Hall or Barracks get more flamethrower squads.