Normal shoe polish - clean them, then brush on and brush off. 5 mins.
Then, for the bit with the mirror shine, get a bottle of Klear floor polish. Open the bottle, get a large wedge of cotton wool and put it over the now open top. Tip the bottle so the polish flows into the cotton wool. Then gently and slowly ‘paint’ the area required with the floor polish. Put a reasonable amount on, but only do it once, so make sure you don’t miss any bits.
It’s fragile stuff, so once it’s dry(10mins or so) , wrap the shoes in something protective. It’s not going to shatter with foot drill, but it marks and scores easily and then sticks out like a sore thumb.
If you can ‘bull’ the area (little circles of polish, then little circles of water), you’ll get a better result for the floor polish to sit on top of. Even 10 mins will produce a very good shine.
Just stay up an hour later bulling them, then have a nap after parade tomorrow. It’s Sunday after all, and we already know who won the F1 championship so not much point watching the race.