This is the 10130th most frequent Turkish word.
başardıklarını
"Başardıklarını" means "what they have achieved."
Başardıklarını here refers to the accomplishments or achievements of the students that were seen by the speaker.
Öğrencilerin başardıklarını görünce çok gururlandım.
I was very proud when I saw what the students achieved.
Başardıklarını in this context denotes the personal achievements or things someone has succeeded in during their life.
Hayatta başardıklarını unutmamalısın.
You should not forget what you have achieved in life.
Başardıklarını here indicates the collective accomplishments of the group that they want to celebrate.