First of all!!! Warmonger with bloodthirst!!!

Napoleon Revolutionary of Persia
For movement and combat strength bonus

Alternative
Xerxes King of Kings of Persia
For base content and another combat strength bonus instead of movement bonus.

Note
Napoleon's units move faster, which might save valuable turns.

Inscribed Sling bullet - +1 Militaristic Attribute Point
Takoba - +1 Combat Strength for all Units in Plains and Desert
Spending the militaristic attribute point for +1 war support might help a bit and if you encounter enemies on plains and desert that will help a lot.

Himiko High Shaman of Greece
For diplomatic and cultural orientation and nothing that boosts their military and expansion

Age
Antiquity

Difficulty
Deity

Game Speed
Online

Map Type
Terra Incognita

Map Size
Tiny

Starting Point
Standard

Age Length
Not relevant

Disaster Intensity
Light

Opponents
1

Start a new game with this setup and restart until you will have a starting point with good production boosts like rivers, hills, woods and resources boosting your unit production like iron. Once you are happy with your starting point save the game.

The most crucial part is the starting point. I had iron, salt, hide and cotton on my successful run. This boosted my units extremely.

The other crucial thing is totally bee lining for the ultimate goal and leave everything else out.

And the third crucial thing is that Himiko won't build second city. If she builds a second city, it will get a lot more complicated but still doable with lots of luck.

Now build a scout and explore until you find Himiko. Now that you know where your opponent is located, reload the initial save.

For techs and civics bee line for Bronze Working and Discipline Mastery, which will enhance your military.
Only produce warriors and slingers from the first turn and nothing else; you will need a lot :) Once gained enough gold, invest in production buildings first, then growth buildings.

Send any unit towards Himiko and attack without hesitation. If you are lucky with your starting point and your capital, you will pump out an unit every first and second turn, which will give Himiko hell. If you are lucky, Himiko will not have built another city when you will capture her capital.

As for her non-military approach you also might encounter just a few hostile units and hope for no independent hostile units around. Fighting any hostile units will quickly deplete your units for those massive difficulty penalties. Don't be surprised if you attack an warrior with another warrior and you will take 80 damage and the hostile unit will just take 15 damage. That was the most extreme outcome I had from such a battle.

On my run I took down the capital with five units loosing three of them in the process. Two slingers and three warriors. Before i declared war I circled the city so I had those five units attacking at the same time without wasting any turn before. Every turn can be crucial. I demolished that pity undefended city on first blood leaving it on like 25% percent. Next turn they reinforced the siege already killing one warrior and heavily damaging a slinger with just three warriors of them. Next round I could damage the garrisoned warrior down to like 15% and then I lost the previously damaged slinger and another warrior. Those two remaining units managed to capture the city in the next round. Only attacking city, even kamikaze style and especially not attacking their supporting warriors outside the city. I was blessed with lots of luck in every aspect.

That strategy took me three attempts and about an hour.

If you like an easy and less luck dependant approach to win on deity, check out my Railroad Tycoon guide.

If you succeed with that strategy and you like this guide, feel free to leave a comment , thumbs up or even a small award as a thank you.

Thanks for everyone succesfully applying this strategy and confirming their results. I'm proud and impressed that some managed to succeed in 20 turns and less.