So, I don't get what's this test of spirit, how do you pass exactly? as I've seen for example 
would pass while 
would fail (don't get the last one tho), I'm curious about how does that work while I'd want to know the aftermath for certain champions I like and why they'd either survive or disappear (
)
While we don't know the specifics of the Test of Spirit, we have some examples to work from. Or, at least to my knowledge, one to work from: Gangplank.
After he was blown to smithereens by Miss Fortune, he turned to Illaoi (they were lovers in the past) for help/comfort/succor. Of course, Illoai being Illaoi, she slapped the soul right out of his mouth. In that story, Gangplank not only survived the trial, but left with a renewed feeling of purpose and motivation.
I think the best way to approach the Trial is to remember that isn't ILLAOI'S trial, but that of her god, Nagakabouros. Illaoi is just preaching the word of the Bearded Lady, after all, that all word is 'Motion'. Nagakabouros is all about moving, fighting, living, laughing...all the things that vibrant life does. And, predictably, is against all things that are stagnant, unmoving, and without change. While the most obvious example of those things can literally be found in anything undead, it is easily applicable to people, and what their trial is like.
For example, Gangplank had suffered a devastating defeat, and was in danger of giving up completely. Giving up, falling down, refusing to get back up and try again? If you're doing those things, you aren't moving forward. You're not growing. So, when he got slapped with the trial, he had to face those parts of himself, and was able to not only rise above those feelings of self loathing and desperation, but find that spark that made him the Reaver King to begin with.
As for how this would effect other champions? It'd be a case-by-case basis, but we can probably ballpark it by looking at their lore and known personality traits.
Braum: Living legend of the Freljord, who is all about helping people and the next great adventure. He obviously loves life and lives to the fullest of his abilities...and Illaoi totally wants that mustache in inappropriate places. Just the fact that she is attracted to him is a great indicator that he'd do fine in the trial.
Jhin: A psychotic killer from Ionia who is obsessed with the number 4 and with all things death. The fact that he is so obsessed with death (dead people don't move) would be a problem in terms of Nagakabouros giving him a pass, but looking at his lore and how he dwells on the past? Insists on things being ordered in a very specific way, and views the world in a very specific way? Add onto the fact that he himself wears a mask, which could be a metaphor for refusing to face himself/theworld/grow? Yeah. He'd have issues there.
Neeko: Is literally all about change in various ways, exploring herself and others on whim. Easy pass.
Swain: Took over an empire and literally changed the course of history in all of Runeterra. Bargained with a demon to gain forbidden knowledge in order to prepare for a grim future. His thirst for knowledge is and power is ambitious as hell, and probably more than enough to pass the test.
Zac: Again, he's literally amorphous and always changing, just on a physical level. Beyond that, lore wise, he is a jovial soul who likes to help others and do the right thing. Likely to pass, but hard to say because there isn't a ton to work off of.
Vel'koz: I'd argue that there are enough similarities between it and Swain (constant quest for knowledge, prepared to do whatever it takes to get that knowledge, ect.) he'd probably do well enough.
Uh. Just my thoughts, anyway.
cough
I feel like, and I'm utterly spitballing and could be entirely wrong here, that the test is supposed to more or less be willing to stand up and fight against immeasurable odds. Braum would be fine as we have seen him literally punch his way through a mountain to save a child, whereas from what we have seen for Jhin, he hasn't shown that he has the will for that kind of thing.
