Dark Souls Remastered | Defeating the Berenike Knight in Undead Burg and getting a Fire Keeper Soul

This is on NG+1 (NG+). Some might say he is a miniboss. Once he's defeated, he never respawns the same playthrough. He doesn't drop anything great, but it's the item behind him (a Fire Keeper Soul) that is very useful. Note that killing him is not technically necessary to loot the item.

A Fire Keeper Soul can be used to reinforce your Estus Flask, which is a permanent effect (even into future playthroughs). You can also consume a Fire Keeper Soul and it will grant 5x Humanity and restore full health (consumption is not recommended until your Estus Flask has already been fully upgraded).

He dropped:

4000 souls
Greataxe
Titanite Shard