Must be done during the story not quick access. If you are struggling with this on Normal then do it on an Easy playthrough and/or equip the following shards:
1. Reckless (fully upgraded you do 35% more damage)
2. Finesse (fully upgraded you have 20% chance to do 50% bonus damage)
3. Lifeforce (you do 30% bonus damage when you are above 50% health)
4. Spirit surge (fully upgraded you do more damage based on how much Spirit Light you have, up to 6000 spirit light)
You can also get another 50% damage boost via two spirit trees.
On your way to meet up with Ku at the end of Act 1, make sure to go up through the first opening above you in the area with the grey one hit kill sludge to meet a guy who gives you a branch for a quest. Make sure to activate spirit well to thr right if him. Warp to town and talk to seed guy, then warp back and talk to him again for a seed, and finally seed guy again). This plants a tree in town that gives you a 25% damage boost.
You can also get another 25% damage boost from a hidden tree near the entrance to Midnight Burrows. The hanging light flowers match the stones nearby to the left (high flower = tallest stone, etc). Bash off them without touching the ground to open Midnight Burrows or the tree to the right. Numbering the flowers 1 2 3 from left to right, the order is 1 2 1 3 3 2 1 to open the tree door, and 1 2 3 3 1 2 1 to open Midnight Burrows. Can be obtained before finishing Act 1.
The Kwolok escape and fight can be seen at 1h 54min in the video below. This is on Easy but without those two 25% damage bonuses (or all but one of those shards), and is still a sub 2 minute kill.