You might ask: why ad crit nidalee? Well to answer that question we need to look at nidalee's cougar Q

As you can see, the AD ratio on it is quite high, but also all the damage that is done from the basic attack of the Q gets converted into magic damage, which basically makes it stronger.
It also mentions that you can lifesteal from the damage it deals.
One thing to not overlook is that this maximum damage that you see, is only when the enemy is low, so if you are full build and you use cougar Q in a full hp enemy, it will barely do any damage, so keep that in mind
Every part of the build does its part, ER is really good early game as you can abuse its procs all the time with the non stop using of the spells. Shieldbow gives you the tankyness (of not only the shield but also the sustain from lifesteal) to be able to jump in and get that cougar Q in a low hp enemy. IE is there because you will need more damage at that point in the game, and BloodThirster is perfect to give you more damage and tankyness at the same time.
Remember that you can proc sheen when throwing a basic attack and using any spell(other than R) as your autos are slow enough.
Her E in human form also gives her attack speed, which makes build AD+crit on her a little better

This build is more flexible and perhaps more reliable than the normal ap nidalee build, as you dont rely completely on landing a spear, it is still important but you can kill people without hitting one.
As you get in range of basic attacks, they will try to dodge your potential Q, but instead of throwing the Q you can keep auto'ing them as they keep trying to dodge your incoming Q, and that way you can kill someone because you are ad crit.
As your cougar Q turns the basic attack into magic damage, sometimes its better to just cougar W+Q instead of the standard cougar W+AA+Q, against someone who has alot of armor, as it will convert the sheen effect into magic damage, and therefore doing more damage than doing the auto cancel.

Though this build looks good, and feels good, it might not be as viable as a normal ap nidalee, as it obviously has less burst than the standard build but it is definitely a fun one to play.