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Boba Fett is a pure, unmodified clone of Jango Fett, the best bounty hunter in the galaxy of his time. This is a reputation that Boba Fett appears to have eventually attained as well. He also has a reputation as a Mandalorian warrior.
That said, we constantly observe in the Clone Wars TV series that although Boba Fett, growing up, is skilled enough to meet job requirements at the level bare essentials, he's always being played out at the end and pushed around.
During the Empire era, we can see him in Jabba's employ. The only time we see him in action, he 1) employed some ingenuity (we can't say if it's a moment of genius or a quality he always had) in tracking down the Millenium Falcon 2) took over the frozen Han Solo from Darth Vader, then successfully got it onto his ship, albeit with Imperial help to slow down his pursuers, and finally 3) when he finally got into a fight, he got thrown into a Sarlacc pit.
From what I know of him alone, I'm not sure it's that impressive a resume. He demonstrated some skills, but always fails at the end no matter how close he gets. Is there anything in Disney canon only I don't know/haven't mentioned that is proof of him deserving his reputation as the best bounty hunter in the galaxy?