Tkachenko, a 7 ft 3 in (2.21 m), 310 lb (140 kg) center, was a great defensive player. He could block out 2-3 opponents to give teammates a chance to grab a rebound. His offensive ability was important too, as his post up moves were basic, but effective, and his shooting was good for a player of his size, with a range of approximately 17 feet.
Tkachenko began playing for Stroitel of the USSR Premiere League during the 1973–74 season, when he was 16 years old. He continued to play for them through the 1981-82 season. In 1983, he began playing for the USSR League CSKA Moscow, and he stayed there through the 1988–89 season. He finished his club career in the former Spanish 2nd division with Guadalajara, in the 1989–90 season.