For time:

3 rounds:
10 handstand push-ups
20 toes-to-bars

2 rounds:

10 strict handstand push-ups
5 rope climbs, 15 feet

1 round:

10 chest-to-wall handstand push-ups
20 muscle-ups

Time cap: 15 minutes

If you are competent with the movements here, grip fatigue will be a major factor, especially on those ring muscle-ups.
Use planned breaks on the movements from the start, especially on the 1st part, as you’ll be back on the toes-to-bar very quickly.
If going to failure on any HSPU is a concern, break these earlier than you think (you can always keep the rest short) as this will ultimately save time vs being stuck at a harder variation.
You can time your rests on the rope with the clock if you know you have a tendency to push too hard or be a bit apprehensive.
The final muscle-ups is where this workout is at, don’t expect to do these in big sets (and if you do, it can be a happy surprise) and you’ll be fine. Just get going and chip away (you’ll be feeling that grip and it might get hard to trust that you’ll get the next rep).

HSPUs (all variations)
Taking short breaks between sets is no problem here (although, you might be going UB if aiming for the semis spot)
Think 6-4, 5-5, 5-3-2 or 4-3-3
If needed, you can do these as fast singles (although with chest-to-wall, ideally, you’ll hit these in sets)
Be clear on the standards to avoid no reps on the top
Pay attention to your shoulder/tricep fatigue (and take short breaks as needed to stay ahead of this)
TOES-TO-BARS
Plan to break these from the start
12-8, 8-7-5, 4 x 5 etc.
Avoid getting too close to failure (especially on grip)

ROPE CLIMBS
Main goal here is to keep chipping away at reps.
Stay focused on the 1st pull to look where the feet go and get a solid/firm grip on the rope with the feet (you’ll want to save your arms as much as you can).
Use the clock/timer for rests if you tend to go too fast/slow on rope climbs
Make sure you’re not pushing close to failure, especially on the 1st round of rope climbs
Shoe selection can matter a lot for rope climbs, make sure to test yours before starting (bring options if possible). If the grip on your shoes “chews” the rope (you’ll get rope stuck on the shoe), clean them between the reps as this will make a big difference on your grip.
If you can, choose a grippy rope (test if multiple options)
RING MUSCLE-UPS
Your grip will be quite fatigued by the time you get here (as well as triceps) so expect these to be harder than you’d think (but approach them with a positive mindset).
Take a short break, chalk and aim to get your 1st set in.
Keep your rest meaningful between sets (15 sec minimum if doing small sets, more if doing bigger sets) so that you actually recover for the next set.
If your hands can handle it (and are not too sweaty), it might be a good idea not to wear grips for these for a better feel.