Glory kills are initiated by getting an enemy low (blinking blue and orange) and melee finishing them. Any enemy type in the game can be killed in this way. The secret to getting this quickly is experimenting the point on the enemies body to melee as different enemies have unique kills in 2-6 locations. Hit different legs, arms, heads, backs, from above, from below. The good news is there are many more than 33 glory kills and can be easily obtained by the end of level two with a small amount of effort.
Later Game: I recommend just for late game progression picking up the faster glory rune. This will help speed combat up while giving you plenty of health and charging the Blood Punch.