Andrei practised various sports from the age of 17, among them basketball, volleyball and boxing, but he turned to sambo after he was introduced to his girlfriend's father, who was a sambo master. Kopylov started training with the renowned Alexander Fedorov and mastered the grappling in a short time, once even submitting his own teacher in a contest. After three months, he was sent to the national junior championships of 1983, in which he won a silver medal. He also won a bronze medal, and in 1985 he finally gained the gold. In 1986, he reached the finals of the USSR championship, being eliminated at the end by the eventual champion, Rotsyavichusom. However, Kopylov obtained revenge over him by beating him in three minutes at the national champion in 1987, ending himself in second place. In 1991, he moved to superheavyweight division, which turned successful for him as he won the USSR championship at that weight in 1991. The same year, after failed plans to move to Canada, he was contacted by Japanese pro wrestling promotion Fighting Network RINGS, and after he accepted, he was sent to the team RINGS Russia, where he met Volk Han, his future partner in the Russian Top Team.
Kopylov debuted in pro wrestling in 1992, obtaining a great submission win over Volk Han. Han retaliated eliminating Kopylov from the Mega Battle Tournament 1995, in which Andrei had taken part after submitting Grom Zaza, but he remained as an important figure in RINGS, having matches with promotion chairman Akira Maeda and his apprentice Tsuyoshi Kohsaka. Kopylov became popular among the Japanese for his anodine looks, featuring moustache, a receding hairline and an unathletic looking build, but those weren't obstacle for his grappling prowess.
After RINGS turned from pro wrestling to MMA, Kopylov struggled to keep the level due to his notorious stamina troubles and age wear, but he got renown after his performance at the King of Kings tournament in 1999. He first faced Leonardo Castello Branco, a heavy favourite to win for being a world champion in Brazilian jiu-jitsu, but Kopylov shockingly submitted him in just 19 seconds with a feint uchi mata transitioned into a kneebar. Not less surprising was his next fight at the event, outstriking Dutch kickboxer Ricardo Fyeet and submitting him in literally half of the time. Kopylov advanced to the semifinals and was pitted against rising star Antônio Rodrigo Nogueira, another famed BJJ stylist who had previously submitted Valentijn Overeem and Andrei's teammate Iouri Kotchkine. Kopylov started the match offensively, countering Nogueira's holds in unorthodox ways and threatening him with a persistent Kimura lock attempt for most of the first round, before Nogueira reversed him and took his back. At the second round, Nogueira chose to fight stand-up and dominated a clearly tired Kopylov, who was fighting without gloves (it took out his usage of closed-fistes strikes according to the ruleset), until the time went out. Two judges claimed draw and a third ruled it for Nogueira, so Kopylov was eliminated from the tournament.
At the next RINGS event, Kopylov met the debuting Ricardo Arona. The stronger and much younger Brazilian controlled the fight via takedowns and position, though he was unable to finish Kopylov due to the Russian's defensive acumen. In an instance, Ricardo accidentally eye-gouged Andrei, which damaged his eye and stunted his performance for the rest of the bout. At the end, Arona was granted a unanimous decision. Notably, one of the judges (Chris Dolman) ruled his judgement of Kopylov as 10 out of 20 for his lack of cardio, which caused laughs among the audience, but Kopylov remained as a fan favorite in the promotion.
Kopylov also fought Ultimate Fighting Championship veteran Dan Severn in RINGS. Kopylov landed several punches thanks to superior hand speed, but Severn used his wrestling background to take him down, which Kopylov countered by flipping him over and threatening with a triangle choke from the top. Shortly after, however, Severn landed a right hook which drew blood from the Russian, before controlling him for a unanimous decision. Andrei's last fight in RINGS was against Tommy Sauer at the opening rounds of the King of Kings 2000. The fight was controversial, as the referee stopped the action when Kopylov seemed to have been knocked out by Sauer, but Kopylov got up instantly and claimed to be unaffected. His team protested for what they called a premature stopping and a lack of comprobation by the ring doctor, but the decision was not reverted.
Kopylov had his last fight in Pride Fighting Championships as part of a special bout against Brazilian Top Team leader Mario Sperry. A substantially aging Kopylov fought defensively on the mat, while Sperry took advantage of the Russian's unfamiliarity with strikes on the ground and landed knee strikes and a soccer kick to the face. Despite a comeback from Andrei with a kneebar which Sperry dove away to avoid, the kick had caused a cut in Kopylov's mouth and the match was stopped to give the win to Sperry.Finishing moves
Reverse heel hook
Kimura lock with neckscissors
Multiple palm strikes