You'll want luck and at least one other person with you. The more people killing the easier it is to pull off. If you're in an area full of players this will be easy.
When fighting enemies you'll notice sometimes they explode into a pillar of light. This will add a counter to the top right of the screen. We need to reach level 8 and that means you need to kill and kill quickly enough so you don't lose your counter. Every time a burst of light happens it will either add another counter or increase a level. We need one counter to reach level 8.
At level 8 a minute timer will trigger.
Get another pillar of light one more time and that will trigger a PSE BURST and thus the Achievement.
This must be done in one area the kill streak won't carry on into a new area in your Quest.