Infinite Research: Advanced Combat Studies, Empowerment

Need to kill any mob with Empowered skill.
You can see an arrow top of his head

These enemies have a permanent buff called Empowerment. These have big golden arrows above their heads. In order to get credit for this quest I have found that you need to kill the enemy while it has the TIMED version of the buff on. So it will say Damage done increased by x% or whatever, and you can see it ticking down. Killing an enemy while it does not have this temporary buff does not count for the quest.

Time seems to have taught me that it's any mob that has a remix buff on it, as long as your character receives the killing blow.

I might just not be the smartest, but this quest was very confusing. I looked for enemies with the "imperious" buff (gold arrow above head). While you're fighting them, they gain a second buff that is "imperiously empowered" that lasts for 10 seconds. You have to kill them within the 10-second window for it to count towards the quest...sometimes. Other times, it seems to simply not give credit without any apparent reason. It also buffs any mobs around it, but those don't count towards the quest, so there's no real point to pulling large groups except to see pretty pretty numbers. Sometimes it gave credit when we didn't think it should as well, so it just seems kind of hit-or-miss with whether you get credit or not.