Not bad as a vague concept but the moveset you've laid out here is, odd even by the standards of this game. It's really just devolved into "Cowboy 2". However, the idea of a character that uses demonic or holy magic as well as guns is cool. There's not much you could do with a normal sword that cowboy isn't already doing though. So I would avoid that to one extent or another. In general given all of the other character concept threads I was also expecting a little higher quality out of something attempting to detail a concept for a fleshed out moveset. If you can't make a detailed well thought out moveset, maybe it'd have just been better to lay out the concept and a few key moves you had in mind.
I feel given this idea there's room to take a more priestly angle to separate this from cowboy. But still keep the guns so it's still recognizably Dante inspired. But that's just my thought.
Viewing post in New character idea: Devil Hunter
My DMC brainrot friend suggested you could take a more Nero esque rout and maybe do a grappler (the combo into grabs type of grappler he says) and gunslinger hybrid.
I say you could go with a more directly religiously themed gunslinger (holy water ala castlevania would be a nice move for this for example) and that'd also be pretty cool.