"It is time to finish with this."
Translation:Es hora de acabar con esto.
I think you are right Fluent. It's sound incredibly strange to use "Es hora" or "Es momento," but I imagine the students of English would be thrown by our use of "time" as well.
"It's high time" or "Time to die" would probably make no sense, and just like everything else of this type it would have to be memorized and logged away.
"Es hora" is an expression.
A good answer here: http://www.spanishdict.com/answers/118988/es-hora-vs-es-la-hora-vs-es-tiempo
Es hora de irnos.= It's about time we left/ it's time to leave.
Es la hora...vámonos. = The time has come for us to leave. /It's the time...let's leave.
Es tiempo de irnos. = Incorrect.
Es hora de...= There's an urgency to do it.
¡Ya era hora! = It was/is about time!