From Halopedia, the Halo wiki
The Elephant can train Marines and you start out with at least some resources, so train all Marines you can possibly have right now. It might even be better to wait a minute and replenish your resources (and thus build more Marines) before you take on the nearby Brutes.
After building a couple marine squads, build some flamethrower units. By this time, the Brutes should send a small patrol. Deal with them, and then replenish any dead or badly injured troops. Wait and build around seven marine squads, and nine flamethrower units. You should kill them squad by squad, or else you WILL get overwhelmed.
When the Brutes are dead (easier said than done), a few Spartans will join you.
Continue west and deal with the infections around the Elephant. Take the whole squad back to the new base which you can get up and running in the meantime.
For this mission, it helps a lot to train flamethrower units. These handle the infection particularly well. Upgrade your Base Turrets with Flamethrowers as well.
Check out the eastern cliffs by sending a few units from the base over and you should be able to find 8th Black Box here. As for the Skull in this level, first kill 750+ infections, then travel back to where the second Elephant was stuck and search the area northeast from here to secure it.
To finish the mission, train an army of Flamethrowers and head south from the base. A little southwest from here are more infections and the second Elephant can be freed. Simply move all three Elephants back to base after you've rescued any ODST Squads. Those can be found at the side-paths of the path that led to the last Elephant.
Whenever all three Elephants are back at the Base, the mission will be over.