The balloon burst in the air. (simple past tense - indicates the bursting happened at one point completely in the past)
The balloon had burst in the air. (past perfect tense - emphasizes that the bursting was completed before some other past event)
The balloon has burst in the air. (present perfect tense - indicates relevance to the present; the focus is on the result of the bursting rather than the exact timing)
Depending on the context and what you want to convey, any of these verb tenses could work:
Simple past shows the action of bursting purely as a past event.
Past perfect situates the bursting relative to some other past event.
Present perfect connects the bursting to the present moment, focusing on the current state resulting from that past action.