Rapid loud tapping in wall adjacent to radiator- when tenant above adjusts
It sounds like you have hot water (hydronic) baseboard radiators, something like this:



Tapping noises in these systems typically happen due to thermal expansion. The copper pipes expand as they heat up. If this expansion causes them to rub against floor/wall penetrations, or on parts within the baseboard radiator itself, you can hear a tapping or knocking noise.

Your video sounds similar to what I'd hear in a previous apartment that had noisy baseboard heat. Luckily, I've installed hydronic baseboard in my current home, and I'm happy to report that it can be completely silent if installed properly. You can also fix a noisy installation, but it will likely require access along the entire route to find and eliminate friction points.

If the noise only appeared recently, it's possible that (1) part of the system that was previously unused is getting used more and (2) changes to the system created a new friction point. Since you said there have been adjustments by a new tenant, it's quite possible both of these apply. For example, the system may have had an air pocket that prevented water flow in a part of the system. Bleeding that air would have started heat flowing and causing more thermal expansion. In addition, getting access to the right valves in order to bleed the radiator could have jostled the fin tube from its supports and created some new friction points.

How to fix it: check along the entire loop and eliminate friction points. The most likely friction points and solutions are:


Fin tube supports. The core of the radiator is a copper tube covered in square aluminum fins. The fins are supported from below, usually by a plastic glide -- part #7 in the example below (source: Haydon Corp.), also visible in the first photo as a piece of gray plastic on the bottom of the fins. If the fin tube has slipped off of one of these glides, it may be resting against one of the metal brackets, which could function like a drum during thermal expansion. To fix, remove the front cover of the baseboard and verify that a glide is in place between each vertical support bracket and the finned tube. The front cover is typically snapped onto vertical brackets at the top and bottom and can be removed by hand with gentle prying. (Note: be careful when handling baseboard radiators - they're full of sharp sheet metal! Gloves are recommended.)


Wall or floor penetrations. The radiator will  be supplied by pipes that usually need to go through walls or floors to reach your boiler and continue to service other parts of the building. When a pipe passes through a wall or floor it should be centered within a hole that provides around 1/4" of space around the pipe, so the pipe does not rub against the opening during thermal movement. If you see a pipe resting on an edge of an opening, you can (a) expand the opening or (b) add something soft to cushion the motion and eliminate the noise. Because expanding an opening is often difficult, a good choice for passing is a small section of pipe insulation, stuffed into the penetration around the pipe. 
Very long runs. If you have a straight run of, say, 50 feet of finned tubing (perhaps going through some walls, but still pretty straight), the expansion may be significant enough that the plastic glides may not be reliable. In these cases, it's best to add a special expansion coupling to break up the long run. This is the most complex of these typical fixes, because the system will have to be drained, pipes cut, and a new fitting installed (typically soldered).


Most likely, your fix doesn't require opening up walls - just a thorough inspection and a few adjustments, and maybe a few inches of pipe insulation strategically placed. A plumber with experience in hydronic heating system should be able to help with this if needed. Good luck!