Well, as usual it depends on what the fiction does with it.
If we go by what the logical consequences would be:
A higher dimensional being would intersect with the 3D plane in what for it is an infinitely thin slice (at most). An infinitely thin cut technically should deal no damage, so they would be virtually unkillable.
Even if the cut does deal damage (cause fiction doesn't care that an infinitely thin cut would just go straight between atoms and do nothing) if the entity in question can survive that particular cut there is no way to deal more damage to it afterwards.
Additionally, if the entity just moves out of the way in higher-dimensional space it would be outside of 3D space completely and hence couldn't be hit with any 3D attacks anymore.
Other way around an attack from a higher-dimensional entity can be quite devastating. For one it would push you into higher dimensional space, which as a 3D being you couldn't really navigate. So that's pretty good BFR.
It technically would also accelerate different parts of your body and atoms a different amount in the directions of the additional dimension(s). Since electromagnetism and strong and weak nuclear force are all 3D forces, the forces responsible for holding your body together wouldn't work anymore once not all parts of your body simultaneously exist in the same infinitely thin 3D slice anymore. This means that a punch from a higher-dimensional direction would probably disintegrate you at a subatomic level.
Also, if your body is higher-dimensional and has a positive 3D density then your body would have infinite mass in total, which might count for something.
So realistically higher-dimensional existence is pretty damn good hax, but I haven't seen a fiction that treats it like this yet.