Back in Action: Apply +2 to your Health. Each time you stand up or are revived by another hero, you may immediately move up to your Speed.

Let's assume that my hero is revived by another hero.

Is it possible that while hero is moving (using Back in Action) he can perform attack in the meantime and later on continue moving (still using Back in Action)?

Personally, I would say no. The card says "immediately move up to your Speed." It's part of resolving the card's effect and the card must be resolved before moving on to the next effect.

The rules for interrupting movement to take another Action pertain specifically to the Move Action. This movement is not a Move Action.

That said, I've been out of the game for a while now and haven't really been keeping up with the official errata, so there may be an official ruling, outside what's written in the rulebook, that contradicts my interpretation.

I agree with Steve-O. Furthermore, that movement doesn't happen during your turn (that is, you would be revived during ANOTHER hero's turn, and if you're standing up, you are explicitly not allowed to take other actions or do other things before the end of your turn)- it doesn't make sense for you to interrupt to perform an action outside of your turn, even if what you were doing was a move action (which it is not).

In short, I'm pretty certain it's a solid, "no."

I am with both of the for the same reasons. I would say no