I checked the wiki to "confirm" but I can't remember it being stated that there are trials to become Chosen, only meeting some criteria. From what I remember it seemed more of a "If an Apostles declares you a Chosen, then you become a Chosen" type of deal. Adding to that I believe Aos said/implied that to be eligible to become a Chosen you have to either be a level 5 or a S rank monster, so before the invention of the serum I suppose it was a given that a superhuman candidate to have already completed all their trials.
Somewhat related but have Alice even completed/been given any trials that we know of? Maybe her learning to fly was one but I don't think the 6th/Aos tasked/suggested her to do that.
As for the Captains, they didn't unknowingly complete their trials. After Henri got to level 5 he provided enough insight/guidance for Bernhardt and Malik to complete their own trials and get their own natural evolutions. None of the other captains did this because it was considered far too risky, hence the development of the serum.
I keep flip-flopping on what I believe that ritual was ment to achieve. Ella said she got her eyes from a ritual and that speech mentions eyes, but she also failed that ritual so did she redo it later? Got a "lesser" version of them? Got them anyway?
It also says "Memories visible" which meshes with earlier theories/guess that the ritual was supposed to increase her Memory lineage and her drinking a liquid that connected her with the 4th while evolving would be a logical way to do it.
Maybe it was both and if she succeeded she would have been able to access memories like the MC but with sight instead of touch?
Also Tanos mechanical copy of her eyes. How/when did he get it? He wouldn't have been able to study them to make it if she got the eyes after she escaped, so did she have them before she escaped? He probably wouldn't mention Ella if he just got the blueprint from the Rebis.
I really hope, but kind of doubt, that this will be explained since this is a relatively tiny detail in the story.
I believe the only known requirements for a natural level 5 are passing the trials, which are different for each person probably. There's likely a sort of "theme" or general logic to the trials since Henri was able to somehow inform Bernhardt and Malik on what they needed to do to pass their own trials.
Michael may be the best example for what the trials might look like since we know of multiple ones he has to accomplish, which include: Absorbing a variety of different types of energy, draining the heat from a planets core and absorbing the energy of a S class monster.
I don't remember if there were others but there is a theme here of absorbing either diverse types of energy and enormous quantity or "quality" of energy. They seem to direct him to use his powers in ways he might not have considered or push him to "gorge" himself past what he would normally have attempted.
As for the other levels, I believe there are no real requirements other than just being strong enough to qualify and stable enough not to monsterify.