I'm pretty sure that historial is used to talk about a person's criminal history, but is it used alone or should it be "historial criminal"?

Thanks.

Or "historial delictivo"...

I agree, it should be possesed by some noun because historial doesn't exclusively pertain to a criminal record.

I've heard "historial penal" as well. I'd say it's a toss-up between historial penal/delictivo, although now that I think about it "historial delictivo" might be the more common of the two.

I heard usually "historial delictivo". But "historial penal" or "historial criminal" are also valid and common.
like Julie & Felipe said, an expert can say "historial penal" is only if you were in jail, or "historial criminal" if you killed someone. Whe need an expert.

Like sosia says, there are probably subtle differences here, just like in English "criminal record" "prison record" etc.