If you get into a straight up name calling battle with Trump, that is where he is comfortable.
You have to really go in at Trump's major fears and hang ups. He needs to be adored because he was rejected by his parents and shipped off to military school because he was a "problem child" hurting animals, hitting his teacher, and generally being difficult. At military school he was berated and broken down, but found some comfort in competition and tests of "manhood" because he was a stronger young guy, usually bigger than other kids.
When he went back into the "upper crust" world that his family's money afforded him (hint, that is an area to mock him: He'd be nothing if he didn't start out with millions of dollars from daddy.). The sophisticated rich people did not accept him. He then went looking for acceptance among the celebrity circuit because those celebrities often come from working class, poor, or middle class backgrounds, were not super sophisticated, and just wanted to enjoy their new found wealth. Still, those people never fully accepted Trump either.
He's this rich guy that always seems on the outside looking in. He gravitates toward Putin, Kim, MBS, and Duterte because they seem to be very powerful men who rule their countries through force of will. They egg him on, but they don't really respect him either.
The fact that President Obama, a black man, who deep down Trump knows is smarter, and more beloved than him, tore him down; stripped him bare in front of an audience that totally got the joke...That stuck with Trump more than any name calling would. He could have rolled with it and laughed at himself, the very way that President Obama was laughing at jokes that had been made at his expense that night. That shows humanity, confidence, the ability to relate to people's vulnerabilities. Everything Trump, for all his money, does not have.