In Shia Islam, the commemoration of the Battle of Karbala is one of the key practices.

During the battle of Karbala the grandson of Muhammad, Hussain bin Ali and most his family were murdered by Ummayad usurpers. They were surrounded and the pretender caliph Yazid demanded an oath of alligience from them but they refused to do so. After making a last stand they were martyred.

The battle and events leading upto it and its aftermath are remembered and mourned through sermons, poetry and songs called Nohas, such as this https://youtu.be/afe-dVqg5k0

Perhaps the most famous ballad about a warrior in China would be that of Mulan. The Ballad of Mulan 木兰诗 was written during that late Southern and Northern dynasties 南北朝, detailing how the girl Mulan went to war on behalf of her elderly father when he was called to serve in the army. She was skilled in battle and brought victory to the war effort, yet when the emperor sought to reward her she only asked that she may return to her hometown. Upon arriving home, her family welcomed her enthusiastically, and her travel companions were astounded to discover she was female.

There's the Song of Roland, the first chanson de geste, written sometime between 1040 and 1100 about the Battle of Ronceveaux in 778. Unlike some later chivalric poems that pay a lot of attention to ritual and symbolism, Roland has lots of blow-by-blow narration. Since the theme is Christians vs Muslims, it was likely popular on the Crusades. Like a lot of troubador poetry, a melody for it does not survive.

The Welsh poem Y Gododdin is a lengthy verse about an attempt by Welshmen to fight off Saxon invaders circa 600 AD, though the oldest surviving text dates to the 13th century (but is believed to be a copy of an older text.) The poem is a tragedy given that only one of the Welsh warriors apparently survived, but it makes an interesting read. You can read the poem in side-by-side Welsh and English text here.