This is a pain, but once again, you can get it on the tutorial world. (The Cobbmeister wrote in the comments that this works MUCH easier if you set your game to Peaceful.) I combined my world with my The Deep End achievement since it's in roughly the same area, and threw Let It Snow for good measure. You obviously don't have to.
In the horse area of the tutorial is a chest with a lead. You only need one. That's the easy part. While you're here, grab as many hay bales as you can to breed the llamas. Also grab some fence and a gate...rip them out of the ground.
Now go due south on the map. I literally carved a hole in the mountain through the start area. You will find a small village on the west side of a savanna. Slightly west is a jungle (good for the ocelot achievement if you need it), and off to the east is a desert area with temples and such. Llamas spawn in the savanna.
When you find the llamas, MAKE SURE YOU TAME THEM.
It's going to be annoying looking for llamas, but they do show up. They're almost always on the slope of the steep hills in this area, and I wandered around and around them until I found two. There are three separate hills in the savanna, so make sure you search all three.
Note that other animals and creatures may keep them from spawning
, so I killed every cow, rabbit, chicken, sheep and mob I saw. I even went so far as to kill the squid in the ocean just off the shore, because I was frustrated I couldn't find any llamas.
I carved out a cavern in the side of one of the hills for a bed and a solid corral for the llamas when I found them. Then I put fencing around the outside. You can do it any way you like, but that's what worked for me. Here are the coordinates of my cavern, which is just so that you know the general area of where the llamas spawned for me.
This is very luck based. You have to wait for not one, but two llamas. On the One, it took about 30 minutes. On the 360, it took hours. Just dumb luck.
You do need 2 llamas, though. Tame them, then use hay bales to put them in Love Mode. (I can just hear Barry White saying that. "Love Mode.") Breed them until there are a total of five. They don't all have to be full grown, but you can't breed them for a little after one is born. It'll take a few in-game days.
Once you have five, you just need to put the lead on one of them, since they all pack together.