Six-Shooter Zul'Jin

TLDR: The tactics are to last until you have 10 mana and cast Zul'jin 2 or 3 times in a row.

The Jeweled Macaw is for turn 1 tempo, and a little RNG. Scavenging Hyena is actually a distraction. If you can win with it, great. But the main purpose is to draw their fire. Pressure Plate is two-fold. At first they instinctively play around secrets. Then it works well as a minion removal and delaying tactic as they work around it. 

The key three cards are Animal Companion, Deadly Shot and Zul'jin. Summon companions and destroy minions as much as possible. You should hopefully have 3 of each by turn 10. You will now gain 3 companions, 5 armour and destroy 3 minions each turn, probably for 3 turns.

For your mulligan, aim to have a 1 and 2 cost in your opening hand for tempo.