Move-up requirements are never mentioned to parents and seem to shift as they are communicated to the girls. Last year, my kid told me that all that was required to move to L4 was a kip or a squat-on. Only one first-year L3 was moved up, and she was the only one who had been allowed to do any uptraining at all during the L3 season. I believe she had all the L4 skills except the vault and maybe the long hang kip. The rest repeated L3, including some who had scored 36s.
This year, my daughter is telling me that they have to have all of the L4 skills by the end of the season to move up. The second-year L3s and a couple of first-years have been doing significant uptraining all season. A few of them already "have" all of the skills except vaulting over the table, for which they are still only doing drills. "Have" at this point ranges from sort of reliable and ugly to very reliable and decent-looking.
She's never mentioned any conditioning requirements to move up, although all of the L3s have their splits down and most of them climb the rope with scissor legs. None of them can do a press handstand, and I don't think they work on them much. They do a fair amount of conditioning, but it doesn't seem to be based on the TOPS program. TOPS is not offered.
In reality, I think move-ups are entirely at the coaches' discretion.