After having dealt a predetermined amount of combo hits on an enemy (set by the enemy type), there will be a series of circles surrounding the enemy. It is at this time that Rengeki will be available by using R1 to activate your Skill Trigger. Using this will deal more damage as well as suspend everything else going on in the battle. Do note that using this on PCs (PvP and Arenas) will generate a Hangeki effect, which is a counterattack and won't satisfy this requirement. In attempting to either max out your Book of 1000 per volume or through running through the dungeons to level up, you will most likely acquire this without much effort. A better goal for these would be from enemies that can take a beating from your attacks and stick around for two or three Rengekis at a time. Higher level areas, or challenging enemies, would be your quickest option, but you will also have to put up with them hitting you hard in return.