Duolingo literal translation rule- she may not like meat = ona może nie lubić mięsa.
Może - maybe, perhaps
Być może - well... actually it's quite synonymous. Could be used here without making any difference, IMO.
Może być - apart from the fact that you will mostly encounter it as two separate words, not a phrase (so it would simply mean "it can be/it may be"), its other meaning is something like "okay fine", "fine with me", "good enough".
Jak ci smakuje zupa? - Może być. (-How do you like the soup? -It's fine.)
Obejrzyjmy "Shreka", ok? - Może być. (-Let's watch "Shrek", ok? - Fine with me.)