Start with the brain... Okay, the brain, the pituitary gland... Okay, we have to bring in a lot more bio than just the brain in order to get brain chemistry just down. For example, behavior changes with the level of activity of one's adrenal glands... Or the amount of alcohol that made it through the gut and into the bloodstream. So, let me try again.
Start with the body. There is some organizational pattern to your body that shapes how thinking happens in your brain and central nervous system. The wiring in your neurons is a big part of it, as is chemistry. All of those patterns encode information; the thinking happens with the patterns more than the substance of the neurons and brain chemistry.
And with that life-ness comes intellectual demands -- drives for sex, food, rest and physical comfort, etc...
Those are a little harder to map to the physics, chemistry, biology, anatomy and neuroscience, but it still seems doable. One level more abstract than just talking about the design of the parts rather than the parts themselves.
It is this level of abstraction that Qabbalists start talking about the nefesh. It's the bit that deals with the emotions that our chemistry sweeps past us, the physical drives and wants.... Basically, everything that is animal or specifically mammalian about our thoughts.
Notice that in this worldview, there is no line between the physical and the metaphysical. It's gradual, more of a spectrum than a dichotomy.
In Qabbalah's model, the Or Ein Sof (the Light of the Infinite One / the Infinite Light) "descends" from world to world, getting implemented in ever more coarse forms. In the Rambam's model (Yesodei haTorah ch. 2) Hashem had a Thought, which had a thought, etc... A chain of intellects that runs down the various classes of angel through the spheres, and eventually down to us. In his Kelalim, the Leshem argues that the similarities are there because these are indeed two different models of same Truth.
And it's a gradualist metaphysics. If we were to continue this train of going up one more level of abstraction after another, we would get to a "world" in which Liberty, Justice, Truth, are more relevant categories for describing why a decision was made than if we tried explaning a person's actions by describing the sodium ion levels and whatnot at various neurons.
It's like answering the question about why a pixel on your monitor went red. You could discuss the gate that flipped in your display in response to a voltage level on the cable, in response to various logic gates flipping inside your computer's video card, etc... Or, you could discuss the notion of trying to balance your checkbook in Excel, and unfortunately, you're overdrawn. Neither are wrong. Neither is more real. However, if you want to solve the real underlying problem in your life, talking about budgeting is more useful.
On the top of the chain of abstraction is Good (as we say in the Shemoneh Esrei "הטוב שמך -- Your name / reputation is 'the Good One'), the Cause of All Existence (to literally translate the tetragrammaton). The Giver of everything, including our very being.
And our connection "10 tefachim below the Throne", is where the neshamah begins.
People are uniquely in the Image of the Divine because we operate on all these different planes at once. We can think about the nefesh's desire for a lava cake and the neshamah's desire to live a meaningful life that advances Good in this world.
And so in the levels between them we have the ruach. Where these desires meet and conflict, we have to think things out. As R Dessler puts it, the nequdas habechirah -- the free-will point -- is at the battle-front between physical desire and Truth. We have conscious thought. If the ruach is in the physical world, and the neshamah is in heaven, the ruach is in the world between our ears.
All of which is gradualist. It's not instead of believing in the brain. It's thinking of the brain as the slide-show on the wall, where the soul is the beam of light that casts the image. (And in this mashal, tzimtzum is the film which blocks the parts of the Or Ein Sof that don't belong in the world, but now I'm going even further afield.)
So, to try to answer your first question:
What is most tzelem E-lokim, Image of the Divine about us is our ability to self-define who we are. It's not the neshamah, it's the tension between the neshamah and the nefesh from which the ruach emerges. No matter how high up the ladder of existence we would go, we would still be infintesimally above zero compare to an Infinite Deity. We balance physical and spiritual, bad and good, and even different goods -- for example the discipline of tact and knowing how to balance Peace and Truth. Our most transcendent aspect is our very ability to transcend. The fact that we can climb, and don't just exist in a single olam, at a single plane of abstraction.
Which means G-d doesn't want it to be easy. The whole thing requires that tension between different ways of looking at the world.
In short: why is it so hard? Because the greatest good is growth, not level.