It seems people have trouble doing this, so I'll give you some ponters.

First off don't even think about trying to kill him until you are level 50!!!
It willl be impossible.
Another thing is to have some good weapons. They don't have to be amazing, but it would help if they are.

Now here's what you wanna do:
1. Go to the Arid Nexus: Boneyard, go up the com tower, and kill
What we're looking to do is make him drop an orange shield called "The Bee".
If he doesn't drop it the first time, save and quit, and do it again.
2. Once you get "The Bee", equip it, and head to Terramorphous peak.
3. Before you blow the horn to call upon Terra, bring in a second player on split screen.
4. Bring that player down with you, and as soon as you drop, go right all the way out to the edge. There will be a ledge around that area that you can go on where Terramorphous won't see your character.
For a clearer description watch this:

5. Now blow the horn and kill dat ho.

If you need help still, or just need better weapons, hit me up, and I can give you some awesome ones.