Lay the Annihilator boss down to sleep and claim the Lightning Hammer.
To fulfil the bonus requirement for this encounter, you’ll need to use a lightning-based weapon to kill the Annihilator. Gear up using anything that provides defence against lightning as that’s pretty much what the boss will use against you for the majority of the battle. Avoid heavy armour where possible. Stay out of his way and he’ll stick to just 2 attacks until his HP gauge is whittled down to half.
You don’t need to worry about the first attack as it’s easily avoidable. He’ll bend down to thrust toward you, but you’ll see this coming so just roll out of the way. For his second attack, he’ll reach back, and then throw his weapon at you. As with the first attack, he makes enough of a song and dance about it for you to get out of the way in plenty of time. After he releases his weapon, dodge it and follow up with a flurry of attacks until it comes boomeranging back to him. You can also pepper him with ranged attacks in between these openings.
When his HP gets down to the halfway mark, he’ll start to use a stun attack and follow up lightning-based projectiles if you’ve failed to put enough distance between the 2 of you before he freezes you. The stun attack is preceded by him raising his hands into the air. When you see this, run like the clappers. If you’re far enough away, you’ll still be stunned, but it will wear off before the Annihilator can deal you any damage. Also, in the latter scenario, his projectile attack won’t be lightning fuelled and will be easily avoidable.
At close range, he’ll employ hard-to-avoid horizontal spin attacks, with good range and speed, so you may want to opt for ranged combat as described above to make life significantly easier.
Once you’ve defeated him, you’ll be awarded with a Big Sealed Rune and Lightning Hammer.