On deity you have to conquer all 28 cities within 37 rounds (compared to 60 rounds in the easiest mode). The game ends when the last city is captured.

For the achivement you have to play in deity mode and you must reach 200 points. You get 5 points per city, this makes 40 cities.
40 minus 28 captured cities minus your starting city makes 11 cities to be build. I think it is a bug, but the last conquered city doesn't count, so it's necessary to build 12 new cities. There is one free settler at the start of the game, so 11 settlers have to be build or bought.

You have to destroy Athens encampment, so that Alexander and Hypaspist can pass (Hetairoi have special ability to ignore enemy ZOC).

Hit the encampment with the Archer in the west.
Take the encampment with the Hypaspist in the west.
Move Alexander to the street in front of Athens
Also move the western Hetairoi to the street in front of Athens and attack Athens.

With the Archer in the east attack Sparda encampment.
It's not needed to destroy this encampment, it will fall anyway when the city falls, but the Archer gets XP for this shot.
Move the Hypaspist in the east towards the Sparda encampment.
Move the remaining Hetairoi onto the hex with the marmor.

Move the settler to the northeast hex of Pella encampment and build a city (further mentioned as "first built city"). Swap the street tile in the south and build encampment there.
The tile next to the wine seems to be a better place for building a city, but you loose one round for getting there and don't have the front position for the encampment.

Build:
Pella: Hetairoi
First built city: Encampment

Screen after first round:

Take Sparda round 2:
Move Hypaspist 1 field towards Sparda
Move Archer 1 field towards Sparda and attack Sparda
Attack Sparda with the Hetairoi
Attack Sparda with the Hypaspist

Take Athens round 2:
Move Archer onto the wonder and attack Athens
Attack Athens with the Hypaspist
Attack Athens with the Hetairoi
Move Alexander one field up

It is neccessary to conquer Athens second. Your army gets fully healed after taking a city with a wonder.

Athens counts as fully usable city. But Sparda and all following cities will count as conquered. Therefore they will not grow. So you can set production to maximum and can "ignore" food income.

Build:
Sparda: Hetairoi
Athens: Encampment repair
First built city: Hypaspist

Screen after second round:

Kill enemies at the front.
Attack with archers first, so the other units don't get damaged too much in their attack.
Move all your close-combat units first and attack second, so every unit gets the flank-bonus.

Bring the units fighting in Athens to the east. Have an eye where to place Alexander at the end of the turn, so every unit gets the movement bonus from him.

Build:
Athens: Repair granary

Screen after third round:

This round you have 6 units that can reach enemies:
2 Hetairois
2 Hypaspists
2 Archers

Use archers first to weaken enemies.
Move all units first and attack second, so every unit gets the flank-bonus.
Use Hypaspist against Spearman. Spearman are stronger against Hetairoi.
Use Hypaspists and Hetairoi for killing enemies, so you gain the points for the Great Generals.

Make use of Alexander's attack bonus. He gives bonus to friendly units within 2 fields. So move Alexander to the front, step by step, fight by fight. But mind that you don't get caught by enemie's ZOC. Additionally Hetairoi get an extra bonus when Alexander is adjacent.

I killed three enemy units this turn and attackedd Gordian once.

Move Alexander back to Sparda after fight, so the other units get his movement bonus for catching up.

Build:
Pella: Catapult
Athens: Hetairoi

Screen after round 4:

take Gordian round 5
take Tarsus round 6
take Thapsacus round 8

Tarsus:
build Hetairoi round 6
buy Catapult round 7

build in round 8:
first built city: settler
Pella: Hetairoi

In round 8 the Catapult built in Pella and the Hypaspist built in the first built city get available. Use them to conquer Halicarnassus in the next few rounds. Time it well, so you can use the conquering wonder to heal your army.

I prefere Catapults over Siege Towers and Battering Rams. There are only a few cities with walls. Catapults bring down the walls very good and can also be used in all the other battles. They are also useful in conquering cities without walls, especially when there is little space for the close-combat units.

ignore Babylon and Susa for now

take Arbela round 10
take Hagmatana round 12

buy a Hetairois at Hagmatana in round 12

You should gain a Great General in round 11, use it for taking Halicarnassus. Use teleporter to bring it from Pella to Sparda.

Halicarnassus should fall round 12. If it is well guarded, it will be later, because you'll have to wait until your Hetairois are produced. This doesn't matter.

After Halicarnassus has fallen, take the Hypaspist and Catapult and add the 3 Hetairois built in Pella, Athens and Tarsus to form the "Egyptian Army". Use them to conquer Tyre, Gaza, Memphis and Theben.

From now on use Athens, Pella and the first built city to build your settlers. Build the next cities to the north and south of Thapsacus. Leave the space near Gordian for the last settlers. You can build up to 9 settlers in this three cities, so you have to buy at least two.

screen after round 12

take Ray round 13
take Ispaham round 13

screen after round 13:

Split your army. Go along the northern road with the norhern army. Go along the southern road with the southern army. Take Alexander, the Catapult and the Hoplits south.

take Parsa round 16
take Shahr-I Qumis round 16

Buy additional Hetairois on the front to increase your armies. And buy a few Hetairois later in the game to Take Babylon and Susa.

I always get a bit careless at the second half of the game. Today i finished conquering at round 33, but didn't had enough settlers at this time. I had to buy 4 and finished game on round 35. So you see, there is some space for making errors or handling with some problems ;-)

This are the paths of the three armies:

Hetairois build the backbone of your army. They have good strength and a lot of movement points.
They generate the important points for gaining Great Generals and they get an extra bonus fighting adjacent to a Great General. They ignore enemy's ZOC and they get one free promotion when built or bought.

Use the right path for promoting the Hetairois. You get bonus on defending against ranged combat and you get a boost fighting injured enemies.

Prefer using Hetairois and Hypaspists for killing enemy units, so you generate a lot of points for gaining Great Generals. You need them early and you need a lot of them.

Great Generals give a bonus on attack strength and movmement to friendly units within 2 fields. Additionally Hetairois get an extra bonus on attack strength from adjacent Great Generals.
During battle, move the Great General to the front, step by step, fight by fight, so each fighting unit gets the attack bonus. But mind that you don't get caught by enemie's ZOC.
Move the Great General backwards after fight, so each unit gets the movement bonus.

Alexander is best. The other Generals are splitted into two types. One with better movement bonus, the others with better bonus onto units' strength. If you have enough Great Generals you can mix them up, to get both bonusses. Though the bonusses don't stack, you'll get the better bonus of each General.

Keep in mind, that Great Generals can teleport between cities.

Move fast, for a steady pace. Take advantage of the streets. Move only along streets. Use the Great Generals wisely to get the movement bonus to each unit. Don't let one fall behind. The movement bonus counts on Great General's position at the start of the turn.

Use Catapults and Archers first. They don't suffer on attack. Use close-combat units second, so they get less damage due to fighting injured enemies.

Use Great Generals wisely, the bonus counts on the current position of the Great General, so you can maximise it's outcome and move the Great General during the battle to get his boost to each single fight.

Move all close-combat units first and attack after all close-combat units are in position, so each unit gets the flank bonus.

Conquered cities except Athens count as occupied. Therefore they will not grow. So you can set production and gold to maximum and can "ignore" food income. Don't even repair the granary.
Build encampments there. Place them wisely, so newly bought units can easily catch up to the front and encampments can be used for healing your units. Finish encampment training as often as possible, with production toggled to maximum you will harvest a lot of gold, and you also get Great General points.

Also consider pillaging to get some extra money


Time when you conquer cities with wonders, all of your units will get restored to fully health when a city with a wonder is captured.
Wait with unit promotions until you need to heal that unit.
Use pillaging to heal your units.
Place units wisely for healing
+20 in city or encampment
+15 in friendly territory
+10 in neutral territory
+5 in enemy territory

Keep Alexander adjacent, when conquering cities with wonders or a palace. You get free units in this case.
I fetched following:
2 Hoplites from Athens
2 Immortals from Parsa
1 Varu from Patala

He Named Them All After Himself?
Settle four cities in Conquests of Alexander on any difficulty.

No More Worlds To Conquer
Win Conquests of Alexander on any difficulty.

You're the Demonstrably Greatest
Achieve the highest possible rank in Conquests of Alexander at Deity difficulty.