Like a Dragon Gaiden: The Man Who Erased His Name PS4 & PS5

This achievement is pretty self explanatory, you'll need to complete all of the Platinum rank Coliseum events. But to unlock them all (specifically the last two Special Events as Calex has mentioned) you first need to progress to Chapter 4, all the way to the point where you first meet up against the Four Kings upon returning to the Castle. Then, you need to beat each of the Kings (unlocking all of the related King Dethroned achievements), then return to Sotenbori, interact with Akame, and access the Requests section of the Akame Network and select Operation Family Welfare. You'll be taken straight to the mission afterwards, toward the hideout of ex-Omi lackeys responsible for stealing Mizorogi's tech equipment. It's generally a rematch of the battle you had with the group the first time in Ashitaba Park. Defeat all the enemies to clear the substory and unlock the final two Platinum special events in the process, which I'll further describe in detail.

The first event, Four Kings, Four Fights, explains enough. Beat each of the Four Kings in one-on-one matches, they're presented in the same order as you faced in your initial boss fights (Dan Brody, Samejima, Justice, and Ugajin). Thankfully they're not so imitating as far as their HP pools go on this one, and you should breeze through, especially if you maxed your stats out to Kiwami status.

The second and last event, Minamida Grand Prix, is a gauntlet of one-on-one battles against robots with movesets based from data gathered from users of the Inner Fighter virtual reality game series (which itself was presented as a playable minigame from Yakuza 3 through 5.) If you notice the music and the visual looks of the robots along with their moves, you'll realize this gauntlet is basically a love letter to long time fans of the franchise: All the robots are emulating the final bosses of the previous mainline Yakuza games, presented in reverse chronological order, as in Yakuza 6 to Yakuza 1/Kiwami (Tsuneo Iwami, Masato Aizawa, Daigo Dojima, Yoshitaka Mine, Ryuji Goda, and Akira Nishikiyama.) Heartwarming sentimentalism and nostalgia aside, the robots aren't any more difficult than the Four Kings Special Event. Defeat all six robots to win, and the achievement should unlock.

This is not a complete solution, just how to unlock the final 2 platinum Special Event matches as either I missed something or it wasn't obvious to me.

Once you have defeated the 4 kings in the Castle go back to Akame and talk to her and choose Network and requests. Choose and complete Operation Family Welfare and the final 2 events will be available at the Castle.

Hope that helps someone.