Hormuz Start Position
Hormuz begins in a difficult position in control of a single province located between the 帖木儿 to the north and 阿曼 to the south, with two cores (the provinces Bahrain and Qatar) under the control of Haasa at the beginning of the game. Haasa, Oman, and 内志 are all potential starting rivals. 舍迈尔 may accept an alliance immediately, while 也门 will usually do so after having relations improved. The Timurids are hostile, but will not usually bother attacking Hormuz; Oman is the greater threat, as they are stronger than Hormuz and may make an alliance capable of challenging the combined forces of Hormuz, Yemen, and Shammar without careful play. Hormuz usually gets a mission at the start of the game to claim the Omani province due south.
Expansion is not actually necessary to attain this achievement; a relatively easy way to get it is to build up the navy to the point that none of Hormuz's neighbors can challenge it in the Persian Gulf. At this point it would be best to get rid of your army and your allies, as they can only lose you warscore. All that's left to do is develop Hormuz and wait until the necessary idea groups are unlocked for the achievement.
Sources of Diplomatic Reputation
Diplomatic reputation can be increased in a variety of ways, though not all of them are available to Hormuz. For Hormuz, its fourth national idea gives +1, as does having a legitimacy of 100 and a statesman advisor, for a total of 3 able to be amassed relatively easily. Trading in ivory can provide another +2 as well, though this will require conquest in Africa. Certain missions can also give a temporary +1 , though these are not guaranteed to happen at a useful time. A third option could be changing Hormuz's religion as several religions (Hinduism: Ganesha cult being one of the more feasible) give +1 and Buddhism with neutral karma can give +2 and so could Fetishism with the right cult, though as Fetishism is pagan converting is extremely complicated. The rest of this guide will leave these three sources of diplomatic reputation out of consideration and focus on other guaranteed sources, but they do exist and may be useful in the right circumstances.
Apart from these sources, the only sources of diplomatic reputation available to Hormuz come from ideas and policies. The fifth idea of both the Diplomatic and Influence idea groups each give +2 , and taking both will make it much easier to get the achievement. With the 3 that Hormuz can get relatively easily this brings the total to 7, requiring an additional 3. From here, policies will be required to increase the total higher, but luckily all but one of the polices that give diplomatic reputation require either Influence or Diplomatic ideas, so only the Aristocratic—Exploration policy (+1 , +1, requires ) involves taking extra idea groups.
Useful Idea Groups
The idea groups that can be taken to give useful polices with Diplomatic or Influence are:
It is generally a good idea to balance idea groups taken between the three categories to help balance technology and minimize corruption, so (at least) three additional idea groups will need to be taken from the above list (it may be easier in some cases to simply take a fourth one to make up for not having 100 legitimacy, being unable to find a statesman advisor, or simply because it is more useful at that point in the game). Activating policies early before having 10 total diplomatic reputation can be useful for the bonuses they provide, but will slow down monarch power generation and delay taking future ideas. It may be preferable to wait to activate them all together once the necessary diplomatic reputation is available.
The main challenge of this achievement comes from staying alive as Hormuz long enough to take enough idea groups to get the necessary 10 diplomatic reputation. If survival can be achieved, then the achievement is mostly a matter of waiting for the monarch power to take the appropriate ideas.
A minor note: overextension and annexing vassals both give a negative penalty to diplomatic reputation, and may delay getting the achievement even if Hormuz has a gross total of +10 otherwise. In the case of overextension, coring all uncored provinces will remove the penalty; the -3 penalty from annexing a vassal will go away after 10 years.
The espionage action, "Sabotage Reputation", also gives a penalty to diplomatic reputation. This becomes available at diplomatic technology 21 (in around 1674), so it is best to aim to finish the achievement before then, if possible.
The Exodus Strategy
Hormuz's position in the Middle East is very tenuous, and it can be difficult to survive the fighting going on in Arabia long enough to get the achievement. For those who merely wish to survive without fighting for their life at every turn, colonization provides a possible solution. Immediately setting the national focus to administrative (with either the Res Publica or Common Sense DLCs enabled), then avoiding spending diplomatic points until Administrative Tech 5 is reached should allow the Exploration idea group and its first three ideas to be taken immediately if the starting 2/4/2 leader does not die. During this time period wars should be avoided and as much money saved up as possible on Hormuz's meager income. Even with the +50% colonial range from the third Exploration idea there are no provinces in colonizing range, but hiring a navigator advisor (easier to get with Common Sense's advisor retiring, but not necessary) for an additional +20% will allow colonization of Mahe in the Indian Ocean. Taking the native repression policy for the +20 global settler increase will help speed up the colonization of the province, as Mahe lacks any native population that could rise up against the colony.
Once Mahe is colonized, several options open up. The islands of Mauritius and Île Bourbon are now both in range, and both have 11 development and few or no natives. Taking them both gives Hormuz a solid base to continue colonizing from even if the original province of Hormuz is lost, and Île Bourbon is also in range to allow fabrication on provinces in Madagascar if expansion there is desired. From here, Hormuz can go either east or west; it's possible to reach the African mainland from here, colonize the South African region long before any Europeans get there, and take a cut of the trade passing through. (This can also allow Hormuz to conquer up the eastern African coast and gain the trading bonus for ivory.) It's also possible to colonize eastwards, using Diego Garcia and Cocos Island as stepping stones, and begin colonizing the rich provinces of the East Indies, again long before anyone else shows up to compete. It's even possible to establish a colonial nation in Australia or New Zealand if desired. The downside of colonizing the East Indies is that eventually the Europeans will show up and start wars for Hormuz's provinces, but it's possible (though not necessarily easy) to hold them off with the aid of allies in the region. (South Africa, by contrast, doesn't seem to inspire as much imperialist aggression except by neighboring African nations.)
Since Hormuz already has Exploration, it may be beneficial to take Aristocratic in order to get the policy with it. Sending a Conquistador to explore the New World can also give useful rewards, and it may even be possible to colonize in the New World. (The only downside is that colonies there won't provide any useful trade to Hormuz unless it also colonizes up the west side of Africa into the Ivory Coast node.) Alternatively, the Exploration group can be abandoned when Hormuz is finished colonizing if the Art of War DLC is enabled, allowing another idea group to be taken in its place.
Spread out around the Indian Ocean, Hormuz should be in a safe enough position to survive long enough to build up the necessary diplomatic reputation to get the achievement.