Using this strategy, I find myself winning all of the 1st and 2nd fights and better than 80% of the 3rd fights. I don’t always win the 3rd fight. But you don’t need to. If you find yourself losing a fight, surrender quickly so that you save your units so that you can fight again quickly. It has happened several times that I lost the 3rd fight only to win it when I tried again.
The hardest 3rd fight to win is the one with 4 Mounted Camel Archers and 4 War Chariots. I usually lose that fight though I do win it on occasion. If you have a 3rd fight that you cannot win after a few tries, make sure that you dismiss the fight before the fights reset. The fights are offered on a 24-hour schedule. If you dismiss it before the reset, you will get a new 3rd fight next time. If you don’t dismiss it, you will keep getting the same 3rd fight over and over again until you win it.
As far as military buildings go, you only need to build 2 Nubian Archery Ranges. It is tempting to build one of each military building but don’t bother. Of the units other than Nubian Archers, War Elephants are the best but they come so late in the settlement that you should be getting ready to wrap the settlement up when they become available. Plus War Elephants take 8 hours to train while Nubian Archers take 4 hours. Don’t mess with the other military units. Only train Nubian Archers.
You will need to build other military buildings to complete quests but you can immediately sell them once the quest is complete. Only building the 2 Nubian Archery Ranges will save you space. I usually get expansions until there are 8 available expansions remaining. I no longer need the extra expansions with the space saved on military buildings, which helps me finish quicker.
And the space you save from building only 2 Nubian Archery Ranges should be used to build as many goods buildings as you can. Even though fighting is central to Egypt, producing goods is what is required to complete the quests in any settlement. I try to have a minimum of 4 goods buildings going at all times. Build as many goods buildings as (1) you can fit with space and (2) you have enough Loot to produce goods in.