This is the 4673rd most frequent Russian word.
достигнутых
"Achieved."
The word 'достигнутыми' is the instrumental plural form of 'достигнутый', used to describe the means or reason for pride in the sentence.
Он гордится достигнутыми успехами.
He is proud of the achievements reached.
The word 'достигнутые' is the nominative plural form of 'достигнутый', used to describe the qualities of the subject 'цели'.
Все достигнутые цели были важными.
All the goals achieved were important.
The word 'достигнутых' is the genitive plural form of 'достигнутый', indicating possession or relation in the sentence.