When you Hunt Prey, your animal companion gains the action’s benefits and your hunter’s edge benefit if you have one.
Ranger: Hunter's Edge: Precision wrote:
The first time you hit your hunted prey in a round, you also deal 1d8 additional precision damage.
Your Animal companion's first hit per round is tracked separately from your first hit, right? Meaning Precision can trigger twice if you and your companion both hit the Prey.