The Peashooter unlocks the Gatling Pea ability at Level 3. I would recommend going for this Trophy in Gardens & Graveyards. It is much longer and should give you enough time to accumulate the 10 player vanquishes needed. As the defender set up near a capture point and pop into Gatling Pea mode and fire away. I got mine at the last capture point of the match.
Note that it cannot be completed in Garden Ops, since it requires you to vanquish players not AI Zombies.