Like a Dragon Gaiden: The Man Who Erased His Name

This achievement can be unlocked by defeating Samejima, who'll be next up after you've beaten Dan Brody (and unlocked the First King Dethroned achievement), unlike the battle with Dan, this one is a straight up one-on-one battle. Samejima stands out in sporting a pair of pistols, thus the majority of his attacks involve these guns. He also holds the Serpent gadget where he can jet boost, generally for defensive purposes in staying out of your striking range, as well as the Firefly gadget where he'll toss cigarette bombs if you're further away.

To start this fight, interact with Dan once again in the Coliseum Reception area, and the ensuing cutscene will see Samejima introduce himself, then the battle begins. His HP pool is much smaller than Dan's, but with his defensive evasion abilities it's harder to land damaging strikes, so it's just a matter of patience and timing in finding attack openings as you stay close to him. But if you really want to make this battle easier, max out your Attack and Heat Gauge+Extreme Heat Mode stats, then smoke in the Coliseum Reception area before the fight until your Gauge is completely full, and activate Extreme Heat while in the Yakuza fight style and mash away with until Samejima is defeated. The achievement should unlock after the post-match cutscene.