It's not clear from the description of Fearsome Duplicate what stops the duplicate. Can it walk through walls? Fly? Swim? Go through the ground to a cavern below? Is it blocked by a thin sheet of lead and so on?
It says you don't need to maintain line of sight or line of effect but it doesn't seem to say what can stop the duplicate itself.
Well if it walks through a wall, you will lose line of effect/sight and lose the duplicate.
As it as a figment illusion, assuming you don't wink out its existence by the above, you can technically manipulate and move it however you want, but doing things that don't fit appearance (like a waterbound theme'd version of yourself flying, or moving through a hostile effect unharmed) can give people chances to disbelieve the illusion (likely with associated +4), at your GM's discretion.
It says you don't need to maintain line of sight or line of effect but it doesn't seem to say what can stop the duplicate itself.
Well if it walks through a wall, you will lose line of effect/sight and lose the duplicate.
It specifically says in the spell that you don't need line of sight/effect.
You can maintain control of your duplicate even if you have no line of sight or line of effect to it.
Other than that I think AwesomenessDog is correct. It can move in any direction, and can go through walls , but doing so will make the illusion less believable. There could be circumstances where doing so would NOT be unbelievable, but you'd have to establish somehow that you can walk through walls in a believable manner.
If the illusion is damaged by an attack or AoE spell, if it goes beyond the maximum range of the spell, or if you stop concentrating it will wink out of existence.
As for things like a sheet of Lead, I'm not sure. Unless there's a general rule about this I assume that rule doesn't apply to this spell. As far as I know that's a specific rule that must be called out by the spell, but there might be a general rule about it.