"На донышке" means a very small amount of vodka, the amount which covers only the bottom of the glass (=чуть-чуть). It became the meme because the girl who declared to be raped drunk a lot obviously.

Понятно спасибо. Необычное выражение для меня. Да, я смотрел все 3 части этой истории, все было понятно кроме этого выражения.

This girl is under the legal age. She was raped. When on this show "Пусть говорят" someone asked "Had you drunk any alcohol?" The girl answered "Yes, it was vodka, but only at the bottom" (на дне/ на донышке) In other words she was poured vodka just a little bit at the bottom