How to Move the rotated Game Object Forward

I have a GameObject that is rotated. Now what i want to do is move the GameObject forward ofcourse after the rotation has already been done.

Now i can easily achieve this using transform.forward.

But the problem how do i do this using a Window->Animation and then setting curves. Animation exposes only Transform Component which has x, y, z which does not work properly as i have the gameobject rotated.

The Same Problem i thought to solve using ITween but the same problem there. How do i use transform.forward there.

What i am trying to achieve is Ping Pong type Animation of a Rotated GameObject, ofcourse on the axis of gameobject after it has been rotated.

Any help would be appreciated Thanks in advance