Recently I've noticed the use of "hero" to be non-gender-specific. 

"Heroine" does have the meaning of a female hero, but it also has this meaning: "the chief female character in a book, play, or movie, who is typically identified with good qualities, and with whom the reader is expected to sympathize."

In the "chief female character" usage, we're not necessarily talking about someone who is saving the world. In fact, sometimes the person is actually a victim waiting to be rescued by a man. For example, Snow White is the heroine character in the Disney movie of the same name.

Probably for that reason, calling a woman that we admire a "heroine" seems like less than a compliment, even though the dictionary definition says otherwise. "Shero" is apparently a new word intended to feminize "hero" while still sounding heroic. I have never heard anyone say it, but it's in the dictionary.

English is slowly abandoning these gender-specific words. Here are other examples of old-fashioned words:

waitress

actress

air hostess

policeman

In modern English we use the masculine words waiter (server, in AmEng) and actor; or the gender-neutral terms flight attendant, police officer.

So to answer your question, "heroine" is definitely not wrong (and neither are the words I wrote above) but it's not very modern. I would pick "hero", as "shero" doesn't sound very standard to me.

Just wait until Hillary Clinton's president, though: I'm not sure the world's ready for Bill to be "first gentleman" instead of "first lady"...will we get "first spouse" instead? We'll see!

I agree with Christine.  

In addition, I have to say that although "Hero" is used frequently - mainly for males (sometimes for females),  "Heroine" is not as frequently used in the spoken English language. (I find it more often used in articles, summaries, etc.)  

Using "Hero" for either male or female these days is acceptable, as is "Heroine" when referring to only the female.

Sorry, you are either going to get into the business or working for police trying to spot criminals,  aren't you? 

Just joking. 

Sorry.