This strategy relies on the fact that everything is set on islands and trade routes are essential for the growth of your settlements. The strategy makes it possible to defeat all three hard NPCs without building a keep or any army. I call it the "Naval Embargo".

First of, save your game. When you're done, cruise across the map and look for a good starting island. The perfect island:

• is large
  
• has cider and hemp (wheat optional)
  
• has 2 or more iron deposits
  
• is set around the middle of the map (NPCs can't start a war if you haven't discovered one of their islands yet, so this minimizes the chance of meeting them)
  
• is close to an oriental island with dates and spices

The islands settled by Giovanni are a perfect example.

If no such islands exist on your map, go back to the menu and start the scenario over.

Once you found your perfect island, reload your original save file and rush to it. Settle both it and your oriental island (take all your wares to the occidental island after building your contor). Now build 2-4 woodcutters, 1-2 fisherman's huts and start with the peasants. Meanwhile, go to Richie Northburg and buy the 50 honor scroll with the honor you got from settling. Take it to Al Zaheer and begin settling your oriental island with the goods you get from him.
Back on your occidental island (I'll call it OcI from now on) rush to citizen level and get your tool production going, if necessary borrow some tools from the oriental island (OrI) or buy them from the trading NPCs (Al Zaheer > Lord Northburgh > Garibaldi, from cheapest to most expensive). On your OrI it's enough to build enough houses to get to the spice farm, once you have that, use the caravel to trade them to your OcI, where you set up a tavern along with the hemp farms.

Once you get your first patricians, start with the bread production chain (2 wheat farms, 1 mill, 1 bakery) and keep upgrading houses manually until you unlock the weapon production. From there on, you can basically stop with your urban development (unless you want more tax income, of course). Now get another iron production chain going to fuel the weapon forge, build 4 more woodcutters and get a rope production chain running.
Once all that is done, build a shipyard and as many small warships as possible.

If you already encountered one of your opponents, which is not at war with another NPC and has a nice island, demand a tribute, and no matter how he reacts, declare war.

The basic idea is to block off all of his trade routes by continously destroying all trading ships. When your fleet reaches the size of about 10 ships, you can start destroying his port and fisherman's huts. Once you destroyed all his property on a strip of beach, leave one of your ships there (as close to the island as possible) to prevent him from building there again. In the meantime, continue building war ships. After a while, the entire island should be surrounded by your ships and the NPC completely unable to sustain any form of civilization (even peasents will move out since they need fish and the NPC can't trade anymore). Now it's just waiting, developing your own islands and banking up money for the next war. The NPC should leave the realm after a while due to massive debt and counts as defeated by you. Two more to go.

In most cases, the NPCs will wage war agains each other, so from the two left one will most likely be weakened. Now you can chose - do you want to remove the biggest threat and kill the stronger one or finish off the weak one?

No matter what you pick, the strategy remains the same - surround the island and starve him on his island.
If the other NPC decides to wage war against you at the same time, call in an auxiliary fleet from Al Zaheer and destroy his ships to cripple his forces.

• Honor - use all your honor (except that necessary to purchase the scrolls to get access to spices) to unlock Al-Zaheers auxiliary fleet upgrades. The fast and strong ships are very helpful in destroying troop transports of a warmongering NPC (e.g. Lucius). On the first level, it's up to you which to pick - I usually go for the trading fleet (extra money) or the items.
  
• Corsairs - don't buy any pacts. With Al's ships you can easily destroy their ships once they appear, which also counts towards the goals of "Imperator" (destroying ships). The Last Contingent is also useful for getting rid of the remaining small warships if you want to upgrade your fleet.
  
• Attainments - Focus on the auxiliary fleets in the beginning. Once all your opponents are defeated, just upgrade what you want.
  
• Natural disasters - In the early game, the chance of a ND is very low, and has the same chance of striking an NPC as you. If a thunderstorm decides to destroy your main island, reload your last save file and hope it doesn't do that again.