How to Train Your Dragon

Dirty sheep will be the key to this one. There likely won't be five brown sheep on the map, but there will be enough dirty sheep combined with brown sheep to get the achievement. As this game's walkthrough advises, begin with the dirty sheep. Pick one up, fly down to the water to wash it off, and drop it off. You basically have a 50/50 chance of it being brown versus white, so just play a couple rounds until the last dirty sheep or two that you drop off turn out to be brown. That way, you have all the "maybes" out of the way and can concentrate on the sheep that are explicitly labeled brown.

A few general tips:

When approaching a sheep to grab it, pause the game (either Start or the Xbox Guide button) as soon as the button combo appears in order to prepare your fingers, then unpause and press the buttons.

You can tap A to speed up your dragon. The circular meter shows its current speed, and the straight meter shows its fatigue. If you fill up the fatigue bar by pressing A too frequently, it will enter a cooldown mode where your dragon will slow down and you'll be unable to boost until the meter is empty. I've found that a pretty good way to maintain speed is to tap the A button twice every time the fatigue bar drops back down to the "i" in "Fatigue". This should keep your speed high without maxing out the fatigue meter.

From my experience, brown sheep will only appear on two islands: the elevated island to the far left (when looking at the sheep pen) and the far back island, on the other side of the double-arched rock formation. The brown sheep icon doesn't appear as easily as the white sheep icon, meaning you need to be closer to the island for it to show up. Try and take stock of how many brown sheep are on each island the first time you visit it. If you pick up a brown sheep from the island and see another one on the island at some point during the animation, you have confirmation that you need to make that trek again.