Nothing changes between this and taming any other normal beast. The only difference is you're looking for a rare beast. Rare beasts when you track them using your hunter's sense they have the yellow smoke trail behind their movements, but they also have a different coloration than their normal counter-parts. For instance the deer will be white instead of brown. You need to just tame a beast that fits this method by baiting it with meat. It'll have an ! above its head if it's interested, once it changes to a hand, walk up crouched down towards the beast and when the QAR appears hit and hold the
until the event completes and the achievement pops.