While you’re out hunting Aragami in God Eater 2: Rage Burst, you will come across some very fast beasts. Some run, some fly, but they’ll all do what they can to create distance between you and them. Bosses will also flee between stages to catch a breather. The only way to keep the melee onslaught going is to chase these beasts down, and to do that you’ll need to sprint.
In order to sprint, simply hold down R1/RB as you move. This eats your stamina (the bottom white bar at the top of the screen). If you allow your stamina to be completely depleted, you’ll stop for a few seconds to catch your breath. Make sure to not let it run out in the middle of battle.
Thankfully, the stamina mechanic is pretty lenient in God Eater 2: Rage Burst. Moving normally, standing still, and not attacking will all allow it fill up. So Sprint for a bit, stop for 3 seconds while continuing to move, then go back to sprinting.