Tirek is cruel and unforgiving, constantly enjoying the torment his victims are put through because of him. He is shown to be sadistic towards humans, and demons alike, not believing much of Sombra's ideals, and considers himself the rightful ruler, unlike him. Psychotic, he will more than happy kill anyone for any reason he could think of, regardless if it truly helps in his goals or not.
Even after being imprisoned, Tirek is easily capable of telepathy, in particular to talk to Sombra during his meditation.
Tirek has a knack of teleporting through summoned portals, capable of appearing and disappearing wherever and whenever he wishes.
Tirek is shown to be exceptionally strong, and easily able to kill with a few well aimed hits.
Tirek was once the king of Tartarus for a fifty year reign, and gained the reputation as the inventor of torture, until Sombra ended up challenging him to a fight, and not only defeating him but putting Tirek under arrest and had him imprisoned rather than killing him.
Tirek doesn't officially appear by name, but he does appear in his telepathy, talking and openly mocking Sombra in a number of instances.
Sombra entered his prison cell in order to check in on him, Tirek cheerfully greeting him. Tirek openly mocked Sombra, saying it will be him who'll take the Surface World, and all he was was a match to start his hellfire. This began to take into effect when Tirek somehow got out, and he reappeared over nearby Central, Amestris, where he was found by Sombra. Before he could capture him, Tirek summoned Pluton and sent him after Central in order to prove what a true demon lord could do, and how easy it was to kill humans.
Sometime after that, he escaped Sombra and later on was summoned by Envy. Instead of helping him though, Tirek mocked and humiliated Envy, calling nothing but a worm and how he was always jealous of Humans despite being a Homunculus. He tried to talk Envy into suicide, but only for the 3-E class to arrive and just manage to drive him away, but only because he had "bigger fish to fry".
He reappeared again, this time inside Nagisa Shiota's dream, and starts to torment him by telling him that he barely ever made any contribution to the team up to that point, and that he was nothing without them. This continued on the next morning, when he lied to Nagisa and showed him all of his friends dead, as a means to torture him even further. Sometime later, he appeared a third time, this time with the attempt to kill Gaara, and even tried to convince Nagisa to kill him for him. However, this only got Nagisa to attack him instead, and cut his horn off, making Tirek disappear.
While roaming the forest, he soon came across Gluttony, finding out that he was looking for him. He told Gluttony he will help him, but backstabs him almost immediately by making Gluttony "pure", and used as his pawn.
Tirek arrived to Central sometime later, attacking Team Harmony while there, and eventually being challenged by Nagisa in a duel. Once challenged, Tirek then showed them Gluttony, and turned the fight into a two-on-one fight, him fighting with Gluttony. At the start of the fight, he appeared to be winning, mocking Nagisa the entire time as he brutally beat him up, but Nagisa turned the tables on him, and made him attack Gluttony in his attempts to fight him. This lead to him losing, and Tirek tells Nagisa that he will never enter heaven due to his actions, before being stabbed in the throat, dying shortly afterwards.
Tirek considered Nagisa as nothing more than another play thing for him, and loved seeing him in pain. He constantly mocked and tormented him as he was away from his friends, all the way up to his death.
Tirek doesn't consider Sombra as much of a ruler, finding him as being nothing but a coward since he constantly followed the rules he established, which Tirek never agreed on. He does get rather upset whenever he's compared to him.
When he was summoned by Envy, he begins to torment him almost immediately, and considers Envy no better than any human. In fact, he considers Envy even lower than Humans, due to his jealousy over them.