Did Imam Hussain (as) know the exact details of what would happen in Karbala or did he just know that he would be martyred?

Imam Hussain (AS) knew definitely that he will be martyred in Karbala and went for his martyrdom because it was the only way to save Islam from deviation and Muslim Ummah from doing astray.

No doubt, Imam Hussain was informed by his grandfather, Prophet Muhammad (SAWA), his mother (SA) , his father (AS) and his brother Imam Hasan (AS) about details of what will happen in Karbala. Allah (SWT) grants His best servants from His knowledge of the Unseen.

source: al-islam