So, it seems to me from the AI, that fastest way is to pick ONE element and kill it, you need 120 points. There are two counters - for Fire / Water elements and Wind / Earth elements.
if you choose, for example, to kill Fire, you'll be increasing your fire / water counter by 2 by each kill
if you make mistake and kill Water element, your counter will decrease by 2
it will also contribute to wind / earth element count - depending on what you're killing - decreasing the earth / wind counter by 1
once you reach 120 points (60 kills), all elements should despaw