To unlock the Man Without Equal trophy in Sekiro: Shadows Die Twice, you will need to defeat all of the bosses in the game. This will require a minimum of two playthroughs.
You can find a full list of the bosses need for this trophy below (credit to Shotgunner on TA). You will encounter the bosses labelled as mandatory whilst progressing through Sekiro's story. The remaining bosses are missable depending on the ending/location. These have been listed in chronological order.
*** Spoiler - click to reveal ***
Gyoubu Oniwa: Mandatory
Lady Butterfly: (missable - hirata estate)
Genichiro Ashina: Mandatory
Guardian Ape: Mandatory
Folding Screen Monkeys: Mandatory
Corrupted Monk: Mandatory
Headless Ape: (missable - Ashina Depths in the room immediately after the poison pool, must defeat guardian ape prior to encountering...mortal blade not required for some reason)
Great Shinobi - Owl: Mandatory - in all non-Shura endings
Corrupted Monk - True Monk: Mandatory - in all non-Shura endings
Divine Dragon: Mandatory - in all non-Shura endings
Demon of Hatred: (missable - Ashina Outskirts near the original gate pathway idol, only appears when the sculptor leaves after the castle is on fire in the end-game of non-Shura endings)
Sword Saint Isshin: Mandatory - in all non-Shura endings
Owl (Father): (Mandatory for Purification ending, can also be encountered, although not mandatory, while doing Immortal Severance and Return endings if criteria for Purification are still met)
Emma, the Gentle Blade + Isshin Ashina: Mandatory - in Shura ending only