In Portuguese I would say "concurso" and not "competição" which has the same meaning as competition in English. In English it seems off to say competition because a competition is more direct, like a sports competition.
It is more succinct to say that you are "applying for a scholarship" instead of appending "competition" or "contest" at the end of the phrase. "Applying for a scholarship" is a colloquial expression that is used far more often than the other phrases.
To address your comment, you would either reference your application or yourself as the applicant. There are two ways of stating this:
My application is very good because I have a strong GPA.
I am a very good applicant because I have a strong GPA.
If what you're refering to is an examination where the goal is to be in the top N applicants, rather than getting a passing grade, then the expression you're looking for is competitive examination.
An examination (competitive or not) usually implies that the candidates submit a written paper or pass oral or practical tests. If the concurso is purely based on candidates sending an application, then competitive examination doesn't work, and something like “scholarship competition” would be better.