Once Fume Knight gets to around 60% health, he'll buff to a second phase; whilst some argue the 2nd phase is easier, if you've worked out Fume Knight's 1st phase attacks, it can potentially be an easier duel.
You MUST ration your Estus
You MUST watch the Ultra Great Sword's condition
From 60% health onwards, the USG will begin to glow orange as it charges, at around 20 seconds of glow-up, Fume Knight will buff, but if you chug an Estus (even if you don't need it), he will 90% of the time aggro and attempt to smash you with the USG, cancelling the buff and resetting the 20 seconds.
You can get all the way through the fight with this method, but even if you get him to 10-20% health before he buffs, the fight is still winnable if you take great care.