She holds the titles of International Master (IM) and Woman Grandmaster (WGM), which FIDE awarded her in 2003 and 1998 respectively.

[1] In 2002, Mkrtchian won the silver medal in the European Individual Women's Championship in Varna, Bulgaria, scoring 8½/11 points.

She participated in the Women's European Team Chess Championship 2003 in Plovdiv, Bulgaria, helping Armenia to win the gold medal.

[2] Mkrtchian took the bronze medal at the 7th European Women's Individual Championship 2006 held in Kuşadası, Turkey, scoring 7½/11 points.

[6] In the 2015 Women's World Team Chess Championship in Chengdu (China) Mkrtchian won the individual gold medal on the second board.