I am an Esperanto beginner. I've been learning Esperanto for a few days on Duolingo and I would like to become good at Esperanto so that I can have the rights to brag about being a polyglot. (I already know how to speak English and Chinese and I'm currently learning Cantonese and Malay as well.) What would be the best best and fastest way to master Esperanto?

Practise.

Acquiring the 'rights to brag about being a polyglot' might not be the best encouragement; it smacks of impatience.