I go on an uncontested battlefield with vi peacekeeper, my opponent plays rengar trophy hunter on it using rengar's reaction speed ambush, can Vi stun the rengar? If yes, who stays at the battlefield?

Yes — Vi still stuns Rengar, and Rengar ends up staying at the battlefield while Vi is recalled to Base.

Moving Vi to an empty battlefield only starts a Non-Combat Showdown, so she doesn't have the Attacker designation yet. Once your opponent plays Rengar there, the showdown converts into a Combat Showdown, and the Attacker is the player whose unit applied Contested — you — so Vi gains the Attacker designation and her "When I attack" trigger fires, stunning Rengar (FAQ #12636). She does need to still be at the battlefield when the trigger resolves.

In the Combat Damage Step, stunned Rengar contributes no Might, so only Vi's 5 damage is assigned to a 6-Might Rengar — not lethal, and he heals in the Combat Cleanup anyway. Because a Defender is still present, the Attacker is recalled (Rule 466.1.a.2): Vi returns to your Base (unharmed), and Rengar's controller remains the only player with units there, so they Establish Control and Conquer.