This is the 11528th most frequent Russian word.
достигшие
"Those who have achieved" or "having reached."
In this sentence, 'достигшие' is a past participle of the verb 'достигать', used to describe people who have completed the action of achieving their goals.
Люди, достигшие своих целей, чувствуют радость.
People who have achieved their goals feel joy.
Here, 'достигшие' qualifies 'спортсмены', indicating those who have achieved the state described in the phrase.
Спортсмены, достигшие вершины своего мастерства, становятся легендами.
Athletes who have reached the peak of their skill become legends.
The word 'достигшие' refers to scientists who have successfully reached their research goals.