Complex sentence: Part of the prize was a singing contract with Johnny Albino and The San Juan Trio and she would go on to record her first "hit" "El Día que nací yo" (The Day I was Born) with the trio.
Split into simpler sentences: Part of the prize was a singing contract with Johnny Albino and The San Juan Trio. She recorded and had her first "hit" "El Día que nací yo" (The Day I was Born) with the trio.