Batalla is product of the River Plate academy, which he joined as a five-year old.[2] In 2015, River Plate accepted a loan offer from La Liga side Real Madrid for Batalla with the option of a permanent move.[3] However, Batalla turned down the move to Real Madrid for personal reasons.[4]
After falling further down the pecking order after the signing of Argentina goalkeeper Franco Armani in January 2018.[9] On 5 January 2018, Batalla signed a one-year loan deal with fellow Argentine Primera División side Atlético Tucumán.[10] After impressing and helping the club progress in the Copa Libertadores,[11] On 25 June, Batalla announced on his social media he would be leaving Atlético Tucumán from his loan spell early.[12]
On 3 January 2024, Batalla joined Spanish La Liga club Granada on loan for the remainder of the season, with the option to make the move permanent.[13] On 23 August, after suffering relegation, he moved to fellow league team Rayo Vallecano also in a temporary deal.[14]