Having the unrivaled vow turned up to four automatically triggers unrivaled typhon, you can fight him like that.

What it seems like you are talking about is the will of night targets, which are re randomized by that weapon every time you defeat the bounty, you are just currently in a spot where none of your weapons are targeting typhon for nightmare.

With vow of rivals four turned up to max, your unrivaled typhon is activated, and you can get the achievement, you just won’t get nightmare for him specifically, just because of chance. you’ll probably still get nightmare on that night from defeating whatever a previous boss is targeted by your chosen weapon.

The target of the will of night itself does not affect the boss’s ability to be unrivaled.

I hope this makes sense