In the last episode, Loki and Sylvie hug ONLY HUG, Loki pushes Sylvie through the portal. Loki destroys all the Kang variants/stores them in a bracelet comic style. Later, after all that they are doing all sorts of chaotic things.
Eg: entering the hp reality in Harry's second year, being a Rachel Dare in another timeline, volunteering for the hunger games, etc. In all these adventures, they are Sherlock Holmes smart but shows off to have people underestimate him, a prankster with the combined brain of the marauders and the Weasley twins and more, has a cool knives, leather thing going on(even in hp) , acts a bit like a member of the Addams family.
In his own timeline, he vandalises the statue of liberty, and other things like that. He also dips stubborn conservatives and capitalists in acid.
Oh, and he's also immune to posion and acid.