This is part of the Grimm Troupe questline.
Start by heading to this location behind a breakable wall in Howling Cliffs:
Use your Dream Nail on a large dead bug at the end of the cave path:
Then go back a screen and attack a fireplace several times to summon the Grimm troupe to Dirtmouth. You'll see their tents to the left of the bench. Go inside and talk to Troupe Master Grimm to receive the Grimmchild charm. Seek out and kill three enemies that are marked with flames on your map while having the charm equipped, then return to Grimm. The familiar granted by the charm will be upgraded and you'll be tasked with defeating three more enemies marked by three new flames on the map. Do so and return to Grimm once more, which will start a battle with him.
Troupe Master Grimm has a few different attacks.
Diving dash: Jump over him to avoid taking damage (you can pogo him as he goes under)
Charge to uppercut: dash away to avoid him (attack him him before he jumps), then avoid the falling projectiles
Cape Spikes: get in between two to avoid damage, then dash towards him to get some damage in
Firebats: jump and dash towards him and attack when within range
At certain health increments, he will take position in the center of the screen and release a torrent of fireballs that must be avoided. Also, after taking enough damage he will stagger (turn into bats and then reappear), which is really the only time you can heal.
Defeating Troupe Master Grimm will unlock this achievement (and advance the questline to the next step).