Battaglia was born and raised in Argentina and is of Italian descent. He spent time in the youth divisions of
Vélez Sársfield and
Almagro before joining
Huracán. He made his professional debut aged 19 in a 3–0 away defeat to
Racing Club in the
Primera División on 3 October 2010. His first goal for the club came on 26 March 2011 in a 2–0 win against
Gimnasia y Esgrima de La Plata. In January 2014, Battaglia joined
S.C. Braga in Portugal, playing 26 games for the club with loan spells in the middle at fellow
Primeira Liga sides
Moreirense and
Chaves, and at his homeland club
Rosario Central. On 15 May 2018, Battaglia and several of his teammates, including coaches, were injured following an attack by around 50 supporters of Sporting at the club's training ground after the team finished third in the league and missed out on the UEFA Champions League qualification. Despite the attack, he and the rest of the team agreed to play in the
Portuguese Cup final scheduled for the following weekend, which they lost to
C.D. Aves. On 27 August 2020, he went to
Deportivo Alavés on loan. On 12 August 2021, Battaglia joined Mallorca on a season-long loan. On 29 July 2022, he joined Mallorca permanently, signing a two-year deal. On 1 April 2023, Battaglia joined Brazilian Série A side
Atlético Mineiro, signing a contract until December 2024. On 30 November 2023, he extended his contract with the club until December 2025. In 2024, he was included in
El País'
South American Team of the Year, playing as a central defender in coach
Gabriel Milito's 3-5-2 formation in Atlético's runners-up campaign at the
Copa Libertadores. On 21 January 2025, Battaglia joined
Boca Juniors on a three-year deal. ==International career==