The film where this character originated, Downfall, portrayed the last 10 days of Hitler's life in the Fuhrerbunker, during the Russian invasion of Berlin. Understandably, with the Russian Red Army at his doorstep, Hitler was a bit stressed which displays itself in ranting at his subordinates for not following his unrealistic orders. Ultimately, he decided to shoot himself, as he felt death would be less humiliating than being captured at the hands of his enemies.
In the parodies however, Hitler is a very hot-tempered man who frequently has violent outburst at even the tiniest tidbit of bad news. This can range from a stupid plot twist in a TV show he likes to a videogame being disappointing. His temper is also tested by his brother in law, Hermann Fegelein, who likes to annoy Hitler by committing antics on him. Another factor contributing to his bad temper are his incompetent generals, who never help in his plans against Fegelein. They rather contradict him, talk about fish or inform him about the most obvious things.
This version of Hitler is also proven to be proficient at hand-to-hand combat, as multiple parodies show him fighting against opponents (usually Fegelein or sent by him) and winning. Or at least putting up a good fight. He even fought Chuck Norris to a standstill on one occasion but lost, because he angered the famous martial artist by punching an innocent girl who tried to stop him from killing Norris.