Adrenaline is used when you sustain enough damage that would kill you, but an ally is nearby to revive you. Essentially, don't die in a level.
This can be obtained on any difficulty level, and can most easily be obtained on the pagoda level (if you sweep around to the far right side as you are escaping). Send your allies into the fray and have them clear out as many enemies as possible if you need help.
EDIT: It would appear that a title update may have prevented the Achievement from being unlocked on the trial level (which is where I originally unlocked it). Or it may have glitched in my favour. In response to the comments from other members who have had no success unlocking the Achievement on that level, I have removed it from the solution. I still recommend the pagoda level.