The important thing to realize when you're writing is that there are very few actual Rules for things like this. Hopefully that's a comfort!
Basically, yes. You absolutely can write from your villain's point of view. I don't think you necessarily need to keep it hyper organized, but you do want to make it clear who's "talking" to your reader.
For example, George R.R. Martin's Song of Ice and Fire series has chapter headers indicating the point of view of that chapter. It's not first-person, but more of a limited third-person narrator, with occasional flashes of omniscience here and there.
You could do chapter headers if you like, or maybe a different font. Perhaps change to italics for that section, or do a header with the character's name. There are a number of different ways of going about it, but ultimately your job is to entertain your reader, who is there to be entertained. 99% of readers won't care quite how you go about it, so long as they're not confused and they are hooked by what they're reading.