For some reason it is possible to reset the timer by only doing the first 3 hits of a combo attack. If you do all 4th the damage threshold will start and if you do 2 then the timer doesn't reset. So the idea is to chain 3x combos with little gaps in between them to allow the timer to reset.
To kill him off quickly you should jump attack him once you knock him down as his timer is long and allows for the extra damage, after that chain 3x combos and finishing the 6th combo set to kill him. The Jump attack is kinda risky timingwise though so you might want to skip it and just keep slashing.
Death Sword has two conditions which cause him to fly away after being knocked to the ground and only one of them has to be true for him to fly away.
The first is a timer that starts counting down once you hit him for the first time, however there is a longer timer if you don't hit him at all but that's unimportant.
The second condition is a damage threshold, when you deal 2 critical moves such as a jump-attack, spin-attack or the 3rd and 4th hit of a combo.
The One cycle abuses the fact that the timer doesn't run down as long as you are slashing you sword, regardless of weather you are hitting him or not.