If it was known exactly what was needed the recruitment process would be a lot more successful than it has historically been - ATC has been around for a long time & no-one has got it right yet.
My take on it is you need to be a good all-rounder - being brilliant in one area & crap in another doesn't work. You need to be able to maintain a good balance of contradictory demands - speed & accuracy, attention to detail without obsessing, flexibility within a rigid framework of rules, confident but aware of your limitations, able to adapt the way you work to suit the situation.
And that's probably what makes it hard to pick - there is no one particular thing that can be easily spotted.
As you say, you can only give it your best shot. I'd add keep plugging & don't give up because sometimes things will suddenly "click" & start making sense.