I made a quick video showing how to beat HV on VMD mode without taking damage (or too much damage). This boss fight can be a bit of a pain, especially in HAH mode... but I believe in HAH mode it is around the same level as in SOS. So it should be easier (as long as you don't get hit more than three times...)
Good luck.
Also, I noticed Vergil's Downfall is a bit harder than the main game. There is a couple of reasons for it... like Vergil not recovering health when in DT, more enemies for each wave (and checkpoints) or the fact that the chains are so much easier and straight forward to use, so (essentially) it is easier to stay in the air with Dante... Vergil is just ridiculously easy to JC 'cus you can literally JC whatever into... whatever... and it happens, and you can just mash the living hell out of your controller and stuff happens so... I dunno. I would like to see people's thoughts in this.
Good luck.
Also, I noticed Vergil's Downfall is a bit harder than the main game. There is a couple of reasons for it... like Vergil not recovering health when in DT, more enemies for each wave (and checkpoints) or the fact that the chains are so much easier and straight forward to use, so (essentially) it is easier to stay in the air with Dante... Vergil is just ridiculously easy to JC 'cus you can literally JC whatever into... whatever... and it happens, and you can just mash the living hell out of your controller and stuff happens so... I dunno. I would like to see people's thoughts in this.