IPA: /ˈpɜːfɪktli/
KK: /ˈpɜr.fɪkt.li/
In a way that is without any flaws or mistakes; completely and thoroughly.
She completed the puzzle perfectly, with no pieces missing.
Perfectly → It is formed from "perfect" (from Latin "perfectus", meaning completed or finished) and "-ly" (meaning in a manner of). The word "perfectly" means in a manner that is complete or without flaws.
Think of something that is 'completed' ('perfect') and done 'in a manner' ('-ly') — that's why perfectly means done without flaws.