I don't know where to start but this is not a drama one will understand with a one time watch.

Story:
This drama involves two parallel worlds, royalty, science fiction, doppelgangers and unexplainable mythical stuff (The flute /deity boy)
The first episodes are slow but tolerable , telling myself that I'm diving into a drama so I need character development and such. Things got out of hand when each character got a look alike (parallel worlds right? using the rule of Yin and Yang) and I had a hard time realising who got switched and to what world. The show doesn't tell what world the characters are in untill it shows either the palace or the Taekwondo center. I was coping up with space traveling between the same timeline but I didn't expect the writer to introduce time travel into the mix. This hurt my head given I was binge watching. So I had to pay extra attention when time travel was introduced, I didn't even have time to notice product advertisements as I was immersed in the story so that I don't get lost. Lee Gon going back in time several times at that, I was like "what the heck am I watching? " . It's not like time and space travelling were new to me but each time Lee Gon time travelled, they were implications, to which some I didn't understand. His arch enemy Lee Lim was a villain but I just didn't understand the motives behind his actions. Any way, if someone has time to rewatch or read recaps after each episode to better understand the story, I would advise one to do so.

Acting:
The acting was good. The actors brought the characters to life especially the guy who acted Jo Young and Eunseop. He's a versatile actor. I could visibly tell the difference between the two guys who had the same face.

Music :
The music was okay. I personally liked Orbit by Hwasa which played at the end of the first two or three episodes.

Rewatch value:
I would recommend it for better comprehension, ofcourse if one has the time, after all it's not a story where everything is laid out for the viewers to figure out.

Romance :
I have to point this out. I didn't like the romance between the leads. To me it was like forced and fast. It doesn't have a foundation as to why Lee Gon would love Tae Eul and him being a monarch and her being a Lieutenant who is not ready to sacrifice her life, career, friends,and family in a parallel world , I just didn't like their love story given that we had a mysterious story we had to rack our brains for. The show would have been better if they were more comrades fighting against a villain who is wrecking havoc between the two worlds than lovers who in the end didn't become a royal couple.

Overall:
If you are someone who wants to put your brain to work. This is a drama for you but if you want to be purely entertained, I wouldn't recommend The King eternal Monarch.