Rain of Arrows — This will decimate AoE clumps when used with empower effects and it being a guaranteed critical strike after rolling. Use this on cooldown to clear trash between boss fights.
Rapid Shot — High damage cooldown that launches three quick shots and staggers targets which opens up a vulernability window to secure kills or interrupt casts.
Penetrating Shot — High damage ability that can be weaved into another heavy shot. This will go through multiple targets. Try to finish off kills with this ability.

Berserk — This is your main DPS cooldown. Try to activate this before large burst damage windows. It will also provide movement speed and self-healing.
Raging Torrent — This will be your only real active weapon ability. It has great single target damage when used with maximum empower stacks, and does have AoE damage potential as it can hit multiple enemies.
Rending Throw — This is your main source of Rend. It is only able to hit one target at a time, but it results in increased damage and is great for boss fights.

It is commonly debated as to whether or not you should take Sweep Sweep or Vault Kick. Having the AoE crowd-control for trash packs with a Sweep Sweep is typically better than single-target stuns.

Attributes

In PvE it is advantageous to lower your Constitution as low as possible and this will be compensated for by having Ward perks. It is recommended to play around 100, but you can go to 50 or lower. The decision is up to you!

The rest of your points should be put into Dexterity.

If you are wanting to mainly use your Hatchet, start putting points into Strength once you hit 300 Dexterity.

Rotation and Priority List

8.1. Single Target Boss Rotation (Bow)

Use Rending Throw.

Dodge and hit a target with a heavy shot into a Penetrating Shot immediately while aiming at the head.

Use Rapid Shot for quick damage.

Continue using heavy shots and maintain your dodge empower buff.

Use Rapid Shot as soon as it is off cooldown.

Do not use Rain of Arrows unless there are additional targets.

Use Berserk as a DPS cooldown or for AoE situations.

If you are about to die, swap to your Hatchet for Defy Death.

8.2. Single Target Boss Rotation (Hatchet)

Use Berserk.

Use Rending Throw to increase damage output.

Light attack until Berserk falls off and goes on cooldown.

Use Raging Torrent to reduce cooldowns.

Light attack with Hatchet.

Swap to Bow to use its abilities if necessary.

If you are about to die, swap to your Hatchet for Defy Death.

8.3. AoE Trash Rotation

Use Berserk and use as many Raging Torrent casts as you can reset.

Dodge and use Rain of Arrows on clumps of enemies.

Follow-up with Penetrating Shot. If this resets, use it again.

Swap back to Hatchet and light attack or use abilities.

New World Damage Type vs Mob Type