[4] In 2012, she won the Group E (women's section of the RSSU Student Grandmaster Cup) of the Moscow Open.

[5][6] In 2013 Batsiashvili won the 3rd Krystyna Hołuj-Radzikowska Memorial in Wrocław, Poland on tiebreak over Joanna Majdan-Gajewska.

[13][14][15] In 2016 Batsiashvili took part in the FIDE Women's Grand Prix series.

[17] In 2022 she won an individual gold medal for her performance at board 2, in the women's tournament at the 44th Chess Olympiad in Chennai, India.

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