source: Best Giant Woman | My Hero Academia | Know Your Meme

make someone's acquaintance (or make the acquaintance of)

meet someone for the first time and become only slightly familiar:

｟かたく｠ A〈人〉と知り合いになる

e.g. they are anxious to make your acquaintance.

I'm delighted ［glad, pleased］ to make your acquaintance.: お目にかかれてうれしく存じます (!... to meet you. と違いへりくだった表現で, 目上の人に使う)