Today I was at my outpost, and saw a momentus. Here is how I killed it: I used my mob launcher to take it out to the water. From there I went under it, and pounded it with my smite 4. It couldn't hit me, and when there where to many minions, I logged out and logged in. I had an anvil ready, so I could enderpearl away from it and repair my armor. In all it took me 10 minutes.
I usually go out with a respiration helmet and do the same thing where I go underwater. The difference is I go deep and pelt it with arrows on an enchanted bow. I pay no attention to the enraged unless they get in my way. Then after I kill the momentus I take out the enraged and get their loot (usually better than the drops from momentus in total). Takes about 5 minutes if nothing goes wrong. My record is about 2 minutes, though that is when momentus was still bugged.
What's a "Mob Launcher?" My girlfriend (MissFyffe48) encountered Momentus once, She apparently died a lot, so she placed a bed decently close to the big guy. She used splash potions of weakness and lava. I don't know how long it took her to defeat him, but she woke me up when she did and collected 20 diamonds. I'm never around when Momentus spawns, but I think I'd just bury myself in a hole lol.
I wouldn't use the flaming mob launcher. Normally, I just chug a zombie virus and go rambo on it until it dies.
Best way: Find Momentus. Tell your friend about it. He lowers its health and dies. You swoop in and kill it and take everything. Tell your friend it despawned. Profit.
One spawned outside my house. Me and my friend cyberazaz101 fought and killed him. He used his "god" sword, and I used my turkey slicer. It didn't take very long. And pigpal102, my other friend, actually found two momentus'. But, he had no weapons, food, nothing. So they both despawned. If I were to be asked a good way to kill him, I'd say hit him underwater with a respiration enchantment.