Strategy
Blackheart is skilled at occupying space through his demon normal moves; hitting fierce or roundhouse summons demons of varying effects. You can use those to keep the opponent busy while building meter and maintaining a lead.
Post-Heart of Darkness Flying Screen Problem
If Blackheart connects with the Heart of Darkness super with non-visible screen space remaining away from him, he will be forced into an auto-dash once the super completes. Very unfortunately, he will be vulnerable during this time and can be punished. Thus you could HoD Cable ... only to have Blackheart dash forward and Cable AHVB'ing that as he recovers first.
To minimize this, Dasrik suggests:
"1. Hold up(back) during the forced dash. This is a simple and reliable method but it won't get Blackheart up as quickly as the second method, so moderately quick Cable players can still shoot you.
2. Do the superjump motion, hard, as soon as Blackheart disappears. This is the quick method, but it's difficult and you only have one or two frames to do it. I'm able to do it reliably enough so that I'll go for HOD on Cable if I need to."