Mehmet the Conqueror Achievement Guide

Anyone attempting Deity scenario achievements in Civ V should start by reading Kolle's guides. The one for Mehmet the Conqueror is located here: http://www.kalle-online.net/blog/renaissance-mehmet-conqueror-steam-achievement-guide/

That guide provides lots of useful tips for this achievement, however it follows a strategy based on winning the entire scenario in terms of victory points, which is not necessary for this achievement. Still, there are two strategies promoted to achieve "Mehmet the Conqueror."

1. Expand south immediately, conquering Jerusalem and Mecca, refusing open borders with the Ayyubids and creating a border wall of forts with fortified units guarding to defend against an inevitable attack from your fellow Islamic empire. This is the strategy Kolle uses in the above guide to win the scenario outright, and if that's your aim then this follow his guide more closely.
2. Strategy 2 focuses all attention on capturing Constantinople with no intention of winning the scenario afterwards, which means you can sacrifice the VP from Jerusalem/Mecca & allow the Ayyubids to gobble up all the prime real estate in the south and east. This involves settling in Anatolia directly and preventing any further settlement by Byzantium so that you have fewer cities to deal with on the way to your goal. This is the strategy I recommend for achievement hunters so I'll go into more detail on it here.

You need to start by adopting Liberty policies, getting an extra worker and the free settler. One worker should focus on building up Aleppo's surroundings, while the other focuses on a road along the coast into Anatolia. There is a hill on the south bank of the first river you come across while moving north (see image). This is where you want to found your city, which hopefully has some good luxuries and/or horses nearby.

Your road should reach this city ASAP, before the worker builds improvements there. After building a few basics (monument, library, and barracks) in Aleppo you need to start churning out troops, mixing between swordsmen, bowmen, and catapults. All units, except maybe one bowman unit, needs to be sent to Anatolia. You need to put pressure on Byzantium quickly, although I waited until about turn 60-70 to declare war, so that I could set up a decent army and functioning economy. You will likely want to settle a third city, either on the Anatolian interior or on the north side along the Black Sea. Avoid the Mediterranean coast completely. This city will take away growing room from your enemy and support additional units for your army. It will require building a settler. Also have a worker build a road west along the southern side of Anatolia towards Nicaea.

Your economy is actually really important in this scenario because the ONLY viable way to conquer Constantinople is with veteran ranged units -- Crossbowmen with logistics and range, same goes for Trebuchets although they are harder to level up (they die more easily). In order to get units with these promotions you'll need to upgrade them by spending gold from surviving bowmen & catapults who have not died in battle. You can train and sacrifice melee units all you want, but your ranged must survive the early fighting to become tanks. Protect your veterans.

This means that the progress you make in moving towards Constantinople will likely be slow, involving some tactical retreats to heal behind melee units. You can put pressure on Nicaea, but it is usually settled in a very defensible terrain, so forward movement will be slow and you should not set up to conquer the city until you have enough units to properly surround it and remove too much attention from any single ranged unit (which can easily die to a city shot + garrisoned ranged unit). You may not be able to take Nicaea until you have Crossbowmen, although it's definitely possible to grab it before then.

Once you've captured Nicaea, use your Great Generals to plonk down a ctiadel northwest, stealing some land and providing a defensive perimeter from the counterattack -- though securing Nicaea long enough to do this may take several turns of back-and-forth conquests and losses between you and your opponent. Don't put the citadel down until you know you can defend the city. When you can spare another General, put a second one down just northwest of the first one, which should take you right to the doorstep of Constantinople (see image). From here, it's a matter of slowly wittling away enemy units while preserving your own veterans -- the coast will be swarming with Dromons or Galleas', both of which are ranged and must be dealt with before you have a safe shot of reaching the city with melee units. Use your shooters to drain Constantiople's HP and rush in with whatever unit can capture a city available to you. Make sure you have built roads leading to the city or your units will get stuck in hills and taken out before they can reach it.

In terms of technology, you should make a bee-line for the military units you'll need. Education would be valuable but you don't have the luxury to obtain it here. Your order should be:

1. Civil Service (Pikemen are the only chance you have against Byzantium's Cataphracts, so you need several by the time you go to war),
2. Guilds (which you will use to spam Trading Posts as soon as they're available, boosting income),
3. Machinery (for the essential Crossbowmen, backbone of this effort),
4. Metal Casting, which leads to,
5. Physics, for Trebuchets.

6 etc) go for Steel and Gundpowder to get Longswordsmen and Janissaries -- although I captured the city Constantinople before getting these, and you probably will too with Strategy #2.

Lastly and importantly: diplomacy is key to surviving long enough to do this. Despite giving up growing room to the Ayubbids, they will still turn hostile unless you actively work with them -- which means bribing them to join your war against Byzantium at all costs. With luck they'll enter a friendship declaration with you, but even if they war against Byzantium they will be pretty useless -- but diverted enough not to smash into your undefended southern border. If that happens you'll need to start over. Bribing Austria or Russia to war against Byzantium is also helpful because it opens multiple fronts for their units to attend to, which means they won't all be right in your face in Anatolia (although it will still feel like it). I delayed Mongolia's expansion into my region by blocking the mountain pass east of the Black Sea with a scout, but when they eventually did I bribed them as well. Better to have a 4-on-1 against your enemy than against you.

Good luck conquering!