I have just played a quick test game for gotm 3, and, me being someone who has never won Monarch or higher on anything other than a duel map before, I would like to share my observations. I hope this is useful, and feel free to say whatever you want, and share your ideas.
1. Barbarians -- I'm not sure if this always happens, but in my game, it seemed there was a specific turn that barbarians started coming. This is more of a problem than it seems, because you don't really get a warning and suddenly there is 3 warriors, and an archer appearing within two turns of each other.
I gotta say that it is very important to either get bronzeworking or archery early, so you can counter the barbarian menace.
2. War -- I started beside Monty, and He definately attacks you quicker on monarch than on prince. 2 turns after i had discovered machinary, having already researched civil service, he declared. Up to this point i had neglected my army, planning on building a mass of samurai, but i hadn't even finished one. He pillaged my lands and slowly i pushed him back, and even captured one of his cities. By now i had severe unhappiness problems. He recaptured and sent a second wave. that wiped me out.
It is crucial, especially if your beside an aggressive opponent, to build your military right away. Never be caught off gaurd.
3. War Weariness -- War weariness has definately been turned up on monarch. Cities become unhappy and start to starve very quickly.
You need to try to keep your wars short and sweet to avoid having your cities riot.
4. Tech Pace -- This wasn't as much of a problem as i expected, at the beggining of the game I went straight for Bronzeworking, hen i got a few other important techs, and then beelined for alphabet. It payed off big time. I was the only one with it, and i was only slightly behind. I traded for all important techs, and made sure i didn't give away alphabet.
This is all i can think of right now, if you have any suggestions, dont hesitate to reply.