Eight destroying Gallifrey and kicking himself out of the the War In Heaven.

Or the Other Inventing Looms, winning the war against the Yssgaroth (Great Vampires), building gallifryan society, helping create Regeneration, being a god, helping set Rassilon up as The God, working with Omega of the first Stelar manipulators and inadvertently leading to Omega ending up stranded in the Anti Matter Universe. So in short yeah the Other. New Who’s Doctors other than Eleven and Twelve have hardly made a major impact on the very fabric of reality

Tough choice between Tennant, Smith and Capaldi.

The 9th doctor accomplished the goal of recovering and moving on from the time war. and even if we are talking about behind the scenes, eccelston helped bring back dr who to the modern audience

I guess all the Trenzalore guff counts as an achievement?

The War Doctor ended the time war