Taming is super easy on Genesis 2. The tek armor helps you tank damage while shooting it in the face with arrows. If you stand against a wall it's even better. When the owl starts torpor running, start flying after it. Wait until it slows down and start shooting while hovering. It won't take long for it to go down.

In my experience, these guys have a slow torpor drain so you should be fine. You can still bring narcotics if you want to be safe.

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