I've been finding Prince to be fairly easy recently, so I've finally made the jump to Monarch and played my first game at the level a few days ago.
I was Elizabeth (nice powerful civ) on a continents-like map. The BCs featured me early expanding until I was attacked by my neighbor Charlemagne in the Classical Era... successfully fought him back (captured a city) and then retaliated with a nice stack, destroying his cities and capitulating him with only a few artic and island cities left way back there.
So at this point I was in a good position, had a nice chunk of good land (slightly more than my neighbors) and considering my neighbors were Mansa Musa and that Inca person, and we all shared a religion, I figured I'd play the game as a tech-trading peaceful builder space race lovefest.
But even with beelining techs and careful trading with the two and an ally overseas... I still found myself constantly falling behind. When the space race came I was dead even with at least three other civs... but it didn't even matter because HC was going for a cultural win! His borders were eating mine up and he was only a few turns away... so I upgraded my early army to Mech. Infantry and unleashed a last ditch strike in which I razed his third culture city.
Of course the war was devastating as his power level was huge... my towns were massacred in a missile barrage and my strike force got destoryed after burning the town. After being able to bribe peace with what
used to be my major science city, I was heavily weakened. HC ended up winning cultural with a fourth city, and even after that I would've narrowly lost the space race in a few turns.
Soooooooo... I decided to redo some history and went back to the big turning point of the game: defeating Charlemagne. This time I marched my army to Inca, upgraded them to macemen and knights. Crippled them taking their strongest cities and took peace. Then my musketmen upgraded to redcoats and I destroyed Mansa Musa in a drawn out war, capitulating him to islands. Then I finished off HC.
So now I own the entire island (surrounded by a ring of vassal cities on islands
), three great capital sites, and began a massive and successful ww2-style invasion to the other continent. The polarity of the two paths of history was stunning.
So you want to do well at monarch? War often and war well.