This is the 80th most frequent Croatian word.
svojim
"Svojim" means "to/with/by one's own" in English, referring to possession or association.
In this sentence, 'svojim' functions as a reflexive possessive adjective that relates the achievements ('postignućima') to the subject of the sentence (my friend).
Moj prijatelj je vrlo ponosan na svojim postignućima.
My friend is very proud of his achievements.
Here, 'svojim' is used to denote possession in a reflexive sense, clarifying that the teacher ('učiteljem') belongs or is related to the people talking.
Razgovarali su sa svojim učiteljem o projektu.
They talked with their teacher about the project.
In this example, 'svojim' establishes the connection between the parents ('roditeljima') and the subject ('she'), emphasizing the reflexive ownership.