To strike or hit each other; to exchange blows or attacks (physically or in contexts like sport/combat).
ボクシングの試合では、両選手が何度も打ち合った。
In the boxing match, both fighters exchanged blows many times.
サッカーの試合は終盤に点を取り合って激しく打ち合った。
In the soccer match, they traded goals in the final stages and battled fiercely.
戦場では歩兵同士が銃で撃ち合う場面があった。
On the battlefield there were scenes where infantrymen fired at each other.