It's not that difficult, you just have to be careful. The parts have to be clean. I prefer solid solder with a separate liquid or gel flux.
That thin brass really transfer heat fast. You have to protect adjacent soldered joints from the heat, or the solder will run out. Because that is on the tank next to the cores and end plate they should be kept cool. Either wet rags or immersing the rest of the radiator in water should work, just leave enough of the bung in the tank exposed so you can solder the petcock back in. The mass of the petcock and bung they will take a fair amount of heat to get them up to soldering temperature, which gives nearby solder plenty of time to melt.
If you notice in the cover picture of the above video, the solder is turning liquid under the paint on the support rod bracket.
Only do this in a well ventilated area, I would even have a fan blowing fresh air on me, the fumes from the flux and the burned coolant can be nasty.