Izuku Midoriya, also known by the hero name Deku, is the protagonist of My Hero Academia and one of the most beloved characters in the story. Izuku began his journey as a propertyless boy; however, his journey was long and complicated.
Over time, he became one of the most important people for the Hero community in general, and he did all this with his own hard work. Over the years he has achieved a great deal and achieved many things that he had never hoped to achieve as a child. With My Hero Academia after ceasing to follow the Final War arc, Izuku continues on his path and continues to achieve greatness as he becomes the greatest of all time.

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Saved Bakugo when no one could
One of Izuku Midoriya's greatest achievements was witnessed by fans very early in the story. It was when Izuku was actually stubborn and was told straight up that he couldn't be a hero. Even so, when Sludge attacked Bakugo, he didn't hesitate or think twice before extending a helping hand to his friend.
Although he had no means to help him or defeat the villain, he still rushed to help, and this in itself is an achievement, because, according to All Might, the greatest sign of being a hero is when your body moves on its own to save people in need. It is thanks to that very act of Izuku that he became the ninth and final user of One For All.
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Mastered One For All
Izuku has achieved quite a lot over time, and it goes without saying that one of his greatest achievements so far has been mastering One For All. Although he hasn't mastered the Quirk 100% yet, he can actually bring out half of its power without much trouble at all. This may not seem impressive; but when you consider the fact that it had only been under him for about a year, Izuku has certainly achieved a lot in this department.
In times of need he can even bring forth all the power of the One for all; however, it would seriously injure him. Later, he managed to bring out all of its powers, thanks to the abilities the remnants gave him.
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Mastered The Other Quirks
Izuku Midoriya is the only user of One For All capable of using the properties of the previous remnants. All Might, the eighth user of One For All, couldn't do it. However, with Izuku, this Quirk has now reached its full potential and being Quirkless, he can bring out the maximum power that has been stored over time in this Quirk.
Izuku had access to six other Quirks that have been stored in One For All, and with each passing generation these powers have grown stronger. The One For All himself grows stronger as it is passed on, and all of these abilities make him far stronger than any other previously left. By the time of the final war arc, Izuku had awakened all of these powers and mastered them to a significant degree.
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Saved Kota
As a hero, the primary job that Izuku Midoriya has on his shoulders is to save lives. He has done that on countless occasions; however, some of them have been more memorable to fans than others. When Izuku fought Muscular to save Kota, it made for a very exciting fight as well as a character moment for him.
Despite being weaker than Muscle, Izuku stood his ground and fought the monstrous villain. He put his body on the line and almost broke every leg to take him down. He did all this to save the life of a small child, and that is truly worthy of respect. In doing so, he also turned Kota's opinion of Heroes and ended up becoming an idol to him.

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Saved Eri
Just as he saved Kota, Izuku also rushed to Eri's rescue when she was introduced to fans during the Shie Hassaikai arc. Eri was beaten by Chisaki, and Deku couldn't stand the thought of her being in misery forever.
He was the one who finally saved her. But what's even more incredible is the fact that he didn't just save her. He involved her in the fight against her abuser and used her power to take him down, which is nothing short of an incredible feat.
Who is that character?

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Fought all for one
As the ninth user of One For All, Izuku was destined to fight against All For One. In Final War Saga, Izuku Midoriya fought against the original All For One for the first time. He also clashed with Shigaraki on a few occasions now. As fans already know, All For One's conscience slowly took over Shigaraki at the end. In fact, for the vast majority of the final war, Shigaraki was simply All For One's extension.
As such, he and Izuku clashed and, surprisingly, Deku held his own against him in battle. Their clash happened at the end of My Hero Academia, and Izuku simply couldn't hold his own in this battle without the remnants. Thanks to a huge sacrifice by the Remnant and later, One For All himself, this battle was won. Everything for one ended up losing and disintegrating. For Izuku to have come this far in just 1 year is truly amazing and deserves praise and respect. He did something even All Might couldn't, and in the process became the #1 hero in the eyes of many, including All Might himself.
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Became the greatest hero
Deku's greatest achievement by far is becoming the greatest hero of all time. Although he hasn't reached the #1 spot, he doesn't need to. Deku has saved Japan and the whole world with it. My Hero Academia starts with Izuku mentioning that it's a story about how he became the greatest hero of all time. This meant that Izuku would undoubtedly always achieve his dream and, in doing so, also surpass his mentor, All Might.
Towards the end, Deku was recognized by All Might as the best hero, and Deku will become the next symbol of peace, which is remarkable for a boy who was born without any quirks. Without a doubt, this will forever remain his greatest achievement and cement his legacy as the greatest in the world of My Hero Academia.
Kohei Horikoshi's My Hero Academia is available to read via Manga Plus.