The way you say it kind of understates the difficulty. It is straightforward to image a large enough satellite if you know where it is going to be. I have even snapped a picture of the ISS with a hobby telescope and a cell phone mount. It's gigantic. Catching a shot of MENTOR 4 is cool, but it's up in GEO and doesn't move much, plus it's just a dot.
The picture of an old CRYSTAL bird is probably the closest thing to the OP in terms of difficulty. The satellite is big and in LEO. The difference between what Ralf did then is that CRYSTAL satellites move less often, so once someone finds them you have more time to wait on good weather. With the X-37, Ralf missed his first shot and by the time he was ready for another try it had already moved, and they had to find it again. That is super tough.
If you have no idea where something went, then the sky is very big and your telescope has a very small field of view, especially if you need to discriminate between different satellites that you see. The fact is, there aren't many techniques for finding secret stuff in orbit. You have two methods (but choose a wavelength)- passive and active- and maybe hacking into a space agency and just stealing the information from a computer. Passive means staring at a lattitude long enough until your satellite passes by and hope you spot it (if it doesn't you either missed it or it has a lower inclination than here you were looking). A smart person might get a computer to help them with the watching, but the task is the same. The problem is that the X-37 is real easy to miss. Even if you see something, it might not be the particular satellite you're hoping for, so you have to filter out all the unwanted things you don't want (usually you can match unwanted things up to known orbits). And even when you see the X-37, you've got to jump on it and track it so you can figure out the new orbit. Active methods are pretty much just radar, and that's out of reach for every amateur astronomer. They might be able to scrounge up some giant apertures but they'll never have the tx power. It's pretty incredible that people are able to do this.
Ralf might have missed it, but like it says in the article, there are volunteers around the world watching out for this thing, and they only needed to track it periodically - and communicate among themselves as a group about their findings - in order to keep tabs on it.
Things get exponentially easier when you've got more hands and eyes on the problem - not to say its not a difficult task, but lets remember - a group of people put it up there (that was pretty hard) - and now a group of people are tracking it.
https://www.space.com/8458-wow-shuttle-space-station-photogr...
https://en.wikipedia.org/wiki/File:USA202_Mentor4.jpg
Hubble-class spy sat imaged, i think by same person: (2010)
https://www.universetoday.com/65458/spying-on-a-hubble-teles...