For this achievement you'll need to defeat 300 enemies with heavy attacks/lock-on fire during your playthrough.
This can be done a few ways, or in combination.
Heavy attacks are used during active fighting, pressing Y in close range of your enemy will execute the attack. This will then leave Asura in an overheated cooldown state.
Lock-On fire is executed during the air scrolling battles. As you sweep the screen for enemies you can accumulate a few and attack them at once by pressing Y when the lock-on reticle is maxed and shining yellow.
Across these 2 methods and following these tactics you should have the achievement during the middle of your playthrough and earn 15G!