Adrenaline fills up slowly when you are in open conflict, but certain actions give you more adrenaline: Getting a hit with a melee/ranged weapon or when an enemy deals damage to Bayek. As it turns out, you don't have to hit only enemies; civilians and animals can also be used. Important characters such as shopkeepers work the best because they are invincible.
This can help with fighting Phylakes, who cannot be instantly killed by an assassination at full health. For the record I didn't do much damage to them in the video because 1. They were a higher level than me (so make sure you at a decent level before going after the Phylakes) and 2. I hadn't purchased overpower perks.