Annubis's Ability

So this is one of those questions about the meaning of "turn". The text on Annubis states, "The first time a non-environment card is destroyed each turn, this card deals the non-environment target with the second highest hp 2 infernal damage." Does "turn" mean environment turn, villain turn, and hero turn? Or does it mean the overall turn--i.e., the "tunr" that starts with the villain and ends with the environment?

What you refer to as "the overall turn" is actually defined as a round.  A round consists of a villain turn, all hero turns in turn order, and an environment turn.  Also, if something refers to a turn without qualifying it, it refers to any turn.  In this case, the first time every villain, hero, and environment turn where a non-environment card is destroyed, Anubis deals damage.

A turn is a villain turn, a hero turn or environment turn. A round starts from villain and ends with environment.

And also to clarify each hero has their own turn. So if you have four heroes in battle and two heroes destroy a environment card on their respective turns then Anubis will activate on both of their turns. So it's best if you want to destroy a lot of environments that you leave it up to one hero to destroy as many as possible so that way Anubis only strikes once, unless of course a villian will be the second highest which is even better.

I believe you mean non-environment cards.

I'm not sure if that is directed at me... When I was refering to the villian being second highest I meant as in that is when you would want multiple heroes to destroy cards, that way Anubis deals additional damage to the villian rather than a hero.

It adresses to you, because you misread Anubis. He deal damage for non-environnement cards destroyed, not for environnement cards destroyed.