Warning:
This thread will contain spoilers for the MHA manga and Anime. You read the below at your own risk.
Origin
Tomura Shigaraki was originally born Tenko Shimura. He was a descendant on Nana Shimura. As a result of Nana Shimura dying this led to Kotaro Shimura (Tenko's father) resenting heroes. Since Tenko Shimura wanted to be a hero this led to him growing up in an abusive household. One day Tenko and his sister snuck into there father's office which lef to Kotaro beating him a bit more than usual.
Later Tenko unlocked his quirk and killed his family (mostly by accident except his father).
Afterwards Tenko Shimura ran away from home. No citizen would help him, and he also got beat up by street thugs. Than he met All For One who did help him and gave him his family's hands to wear. He kills some thugs, and than is given the name "Tomura Shigaraki".
Tomura=To Mourn. It is used when we grieve or say goodbye to the dead
Shigaraki=All For One's last name.
Strength
Shigaraki casually chokes Deku with only a few fingers:
Durability/Stamina/Pain Tolerance
Shigaraki is shot in the hand, along with both arms and legs and is still conscious after:
Shortly after being shot by Snipes he gets stabbed by Stain and shrugs that off. His wounds from Snipes had just healed.
Shigaraki has his hand crushed and remains conscious
Shigaraki and the League of Villains fight Gigantomachia for a month and a half. Shigaraki barely sleeps during this time as Gigantomachia would track him down with his enhanced senses.
Later the league fights Re-Destro's liberation army which has 100,000 people in it. I wont upload the whole fight because its an entire arc (chapters 224-239 basically), but I will upload this scan to highlight Shigaraki's condition. But basically Shigaraki was so tired he was hallucinating mid-fight and was vomiting as well:
Shigaraki takes a blast to the face from Bakugo:
Takes a finger flick from Re-destro which sends him flying several ft:
Takes a hit from 80% Re-Destro. He does partially decay the blast Re-Destro hits him with but considering the blast still levels a city block its still impressive. A tired and injured Shigaraki gets back up:
Speed
Shigaraki blitzes Tsyu from a far distance:
Shigaraki catches Eraserhead's sash:
Shigaraki Blitzes fodder while vomiting and exhausted:
Shigaraki seemingly was able to react to Gran Torino (hard to say for sure because all for one interfered).
Shigaraki nearly blitzes overhaul until one of Overhaul's minions intercepts the blitz:
An exhausted Shigaraki dodges various projectiles from the liberation army:
Shigaraki's double created by twice keeps up with Re-Destro who at his lowest stress output could move faster than the eye:
Even when Re-Destro goes to 100% of his full power Shigaraki can still react and keep up:
Re-Destro comments that with his current physicals, Shigaraki should have been able to kill a hero or two at Kamino:
Skill
Re-Destro comments that Shigaraki's technique has little to no wind up and that his movements are lithe like a cat's. And also comments that Shigaraki has trained his movements, and that type of skill could only be achieved through life or death training for an extended period of time:
Quirk
Shigaraki decays 2 guys instantly:
Shigaraki decays Overhaul's arms instantly, and cuts them off before the decay can spread:
Due to the trauma of his origin, Shigaraki repressed his memories and also kept his quirk in check, limiting it:
Initially before limiting the power of his quirk, Shigaraki was able to decay the surrounding environment, kill from a distance, and cause his house to decay via chain effect:
As his memories started coming back to him, he started limiting his quirk less:
Shigaraki decays an entire building by touching it:
Shigaraki can even decay 100% of Re-Destro's stress which is enough to level multiple city blocks:
Shigaraki can decay people as durable as Re-Destro, who survived a massive fall at lower stress levels. Also he no longer needs 5 fingers to decay stuff:
Shigaraki causes decay with his feet:
Shigaraki erases a city block, and takes Re-Destro's legs:
Intelligence
Shigaraki analyzes Eraserhead and figures out his tell:
Shigaraki has the foresight to see that Compress made a mistake charging Overhaul:
The police acknowledge that with each plan, Shigaraki's are getting more intricate. Also they realize that Shigaraki's plans are targeting the effect he has on society as a whole:
Shigaraki misdirects the sand hero Snatch. He jumps at him which allows Compress to throw a rock under the car Snatch is on:
Shigaraki leaves Overhaul for dead after taking his arms. I'm posting this mostly to show Shigaraki was the one who got what he wanted out of his alliance with overhaul:
Fear/Respect
Shigaraki intimidates Sain, and Stain acknowledges Shigaraki has conviction.
Deku tries to tell Shigaraki that if he kills him a pro will show up and stop him, but Shigaraki just tells him he could kill 20-30 people before that happens. Deku is terrified of that thought and decides to talk to Shigaraki:
Deku realizes he done fucked up:
Shigaraki intimidates the meta human liberation army who were raised since birth to be willing to die for Destro's cause. Even when there spirits are amplified by Trumpet they still can't bring themselves to attack him due to there fear. He also ultimately earns the respect of Gigantomachia, who is reminded of All For One. Re-Destro also submits control of his army to Shigaraki, saying that if they were to attack Shigaraki it would only result in more pointless death:
Awesome