He'd assessed his own injury by realizing that, because he wasn't bleeding from his mouth, he wasn't mortally wounded. The speech he gave lasted an hour and a half with the opening line shown above. The bullet passed through both his eyeglass case and the folded-up speech, so it didn't penetrate very far. Given that McKinley and Garfield had both died not from their assassins' bullets but from surgical complications, Roosevelt reasoned that it was safer to tell his doctors not to remove the bullet but just leave it in place. He was right.
He once killed a cougar. In a knife fight. note He had the knife, not the cougar. Although I wouldn't put it past him to teach one how to fight with a knife.
"Theodore Rex" tells more: "Last Winter, in Colorado, he had leaped off his horse into a pack of hounds, kicked them aside, and knifed a cougar to death. What a great fight that had been!"
His crossing of the River of Doubt, after which it was renamed The River of Unquestionable Certainty. And then to the "Roosevelt River".
His boat was stolen once; he built another boat and hunted the thieves down. Instead of shooting them in the middle of the woods, he hauled them to town for court, going for 40 hours without sleep. He read Tolstoy to keep himself awake.
Even better: when he finished reading Tolstoy, Roosevelt literally forced one of the robbers to lend him a book that he had been carrying. The guy who'd tried to get away with robbing TR was now forced to "volunteer" his book for his intended victim's reading leisure. This—on top of arresting him—pretty much means that Teddy completely and utterly humiliated the robbers.
After he received letters from army cavalrymen complaining about having to ride 25 miles a day for training, in response, Teddy rode horseback for 100 miles, from sunrise to sunset, at 51 years old, effectively rescinding anyone's right to complain about anything, ever again.
During his time in the badlands he once walked into a hotel when a drunken cowboy was shooting up the bar-room with a pair of revolvers. The drunk noticed him, called him "Four eyes", and said that "Four eyes is going to treat." Theodore ignored him and sat down at the bar, but the drunk came over to him, gun in each hand, and repeated his command. Theodore then said "Well, if I've got to, I've got to," and KO'd the drunk in three punches.
Awesomeness by Analysis: as an experienced hunter and military man, he fully understood alcohol will ruin a shooter's accuracy, and also that holding two guns even as your hands tremble from drunkenness is even worse.
Before he became president, while he was away on a hunting trip, someone hired a man named Paddock to either scare him off his land or just shoot him off it. When Teddy came back and found out that Paddock had been hired to kill him, he personally went to Paddock's house and told him "I understand you have threatened to kill me on sight. I have come over to see when you want to begin the killing.” Obviously, the threats ended then and there.
During his time as the head of New York City Police Commissioners in 1894, at a time when the NYPD was at its most corrupt. He more or less singlehandedly ended much of the political and criminal corruption in the NYPD and issued many new reforms, such as giving NYPD officers firearms, had telephones installed in station houses, made officers take regular firearms and fitness exams and hired more than 1,200 officers based on their qualifications, not their political connections. He even got a reputation for walking around the city late at night and in the early morning walking the beat of patrol officers to catch the ones who were nodding off and keep the rest on their toes. In summation: Theodore Roosevelt was a real-life Commissioner Gordon.
During the Spanish-American War, he led a charge against an enemy position on San Juan Hill, showing way more calmness about being shot at than any man should. Especially since he was the only man on horseback, making him by far the most conspicuous target in the American ranks. After he reached the top, he proceeded to draw his revolver and kill an enemy gunner, clearing the way for his men and eventually getting him a Medal of Honor. When you are charging alongside John J. Pershing (who himself earned the Silver Star!) and you make people even forget "Black Jack" was there, You. Are. Bad. Ass.
It's not well known, given his well-earned reputation as a badass, but as a child Theodore Roosevelt was thin and sickly from severe asthma. Through sheer willpower and physical exertion, he overcame his hereditary shortcomings and became a true man's man.