For about two months, I considered Monarch hard. It took a fair amount of growing pains for me to get used to that level - for me, it's been the biggest and toughest jump to date (I haven't made the immortal-deity jump). Going from warriors to archers is a big adjustment for the player, and really learning how to time things more becomes critical. Notable adjustments:
1. You really need to sell out on the early rush - focus on the tech that unlocks your rush unit, and whip/chop aggressively to get them out to take out the AI.
2. Tech path needs to get tighter. For me, this started to click when I got away from the religious path, stopped bothering with oracle, and learned to head towards alpha, aesthetics, lit, currency and COL. Those are the most critical techs post-worker techs (monarchy as well in some situations, but I often trade for that). From there, getting ready to practice the lib race is important.
3. Early specialists can make a difference. I really try to run 2 scientists in my library city as fast as I can - in a lot of games, I want that academy, the philo bulb, and possibly even part of education.
4. Being aggressive when you have the edge. I really started to learn this one at the end of mastering monarch. For example, if I'm able to hit steel first, I'm willing to whip like crazy in all but my best research city to get cannons out fast as possible. If you can hit a civ or two with cannons pre-longbows, you'll blow them away with few casualties.
Really, it all comes down to getting the timing tighter to move up to that level. I suspect most will say that prince-monarch was a difficult jump to them, but it's very satisfying once you do it and keep improving - now monarch games feel easy, but it took a lot of work to get there.