So when you have an ocelot, try to get it into a pen to make this a whole lot easier. You'll also need fish, which you can use the fishing rod to obtain in a body of water. (There's also an achievement world you can download to your device that has all of this set up for you, alongside a whole bunch of other achievements. You can find the world in the forums for this game on TA)
The key with the ocelot is to enter the pen with the fish equipped and then stay still. The ocelot will run around scared if you're moving, but as you stay still, it will slowly approach you. When it's close enough to you, you will see a small button on screen that says "Tame". I've found getting this button to show up is a little fidgety at times in the Pocket Edition of Minecraft (normally this would be mapped to a button on the console version, which makes this achievement a lot easier). You can also push and hold on the ocelot itself with the fish to tame it, but this method is a lot harder because half the time you end up hitting it by mistake, and then you'll have to wait for it to calm down. My best advice with this one, as I said, is to move the screen around slowly when the ocelot has approached you until you get the "Tame" button to show up.
Note that your taming action can whiff, so I would go in with a few fish just so that you don't have to waste time going to get more fish if you fail. Hope this helps!