When speaking in the past continuous tense to refer to background events, 'when' and 'while' are generally interchangeable. However, in other uses, 'when' uniquely refers to the occurrence of a fixed moment or event (eg "when the bus arrived", or "when the plane landed"). This is different from the use of "while" which we would use to indicate that something happened during an event that happened over a length of time (eg "while the plane was landing, the wing dropped off").
Moving to your example, if you were speaking about events that occurred in the past, in a specific class, you would use 'while' (eg "while in class today I caught her chewing gum"). However, in the context of a school report, you are not simply referring to past events but making generalised statements based on past events. You also want to be clear that their trying hard is because of the competition, and that it isn't merely a background event. For that reason, you should use 'when':
She... does her best when participating in competitions, skits, games and any other activities in class.
One thing to bear in mind - a problem a child in education could have is that they are present in class or for an activity, but not necessarily participating in it. If your intention is to state that the student always tries hard during a particular lesson, you need to make sure that the language you use doesn't imply that sometimes they participate and sometimes not. If, for example, you said:
When participating in class she tries hard.
This could be taken to mean that, on other occasions, she doesn't participate in games. It could be better to say "she always participates in class and tries hard".
