Costache may be considered the earliest pioneer of specialised 50 freestyle sprinting for women. She first set the World Record for the 50 metre freestyle when competing at the Romanian National Championships in Bucharest on 16 July 1986. Her time was 25.50 seconds, set in a preliminary heat.
Her achievements at the 1988 Summer Olympics two years later were less successful. Although qualifying for the final of the 50 metre freestyle, she could manage no better than sixth place in a time of 25.80 seconds, 0.52 seconds slower than her personal best.
She competed in the 100 metre freestyle in Seoul also, but did no better than 8th place in the B Final with a time of 57.11 seconds. Her preliminary time was slightly better at 56.79 seconds.