*This solution was written with the original, "Insane" difficulty in mind. This should also translate to Easy Mode - in which you can also earn the achievements.*
I've come up with a solution that takes advantage of the creature's attack patterns to keep you safe from all his shots. The basics of the battle are:
- Grab the drill.
- Drill a head until the crystal is gone.
- Return to the items and grab the sword.
- Hit the uncovered head three times and the head dies.
The hard part is to avoid the attacks - and it seems mostly random, but I assure you there's a definite pattern you can use to make his attacking pretty easy to deal with.
Basically before the "bullet-hell" bit, take up position on the top or bottom of the level half way between the creature and the items. From there, when it starts shooting, move left and then towards the items and you should be able to dodge all of the shots. Using this method I survived for five minutes without killing a single head (just to see if it was as safe as I thought).
You can also start from the centre next to the items and work your way up/down and forward.
When the 8 heads are destroyed, grab the bow and sit in the bottom-right corner taking shots at him. You should only have to dodge two or three energy bolts this way and depending on your accuracy you'll be done in less than a minute after killing the final head.
For those wanting more details, watch this video I put together (it's definitely easier to show than explain):