Seven Cities of Cibola is an easy achievement with many ways to get it. With the Common Sense DLC, player can do it by the quickest but also the most boring way, declare no-causi-belli war on Navajo, Pima, and Apache as long as Apache and Pima didn’t migrate away from you. With Pueblo, these four tribes total have 7 provinces and that’s all needed and raise all of their development to 10. Although raising one development cost 100+ monarch points with natives government + desert/mountain terrain and you need to raise all of them to 10, it is not going to be that hard. Like what are you going to do with those monarch points anyway, raise technology level?
For players who have the Conquest of Paradise DLC, you can play around with the native tech tree, buildings to raise tax and production income and help fund the colonization. This will be one of the long but interesting way to get this achievement, and I did it this way.
I only declared war on humiliation rival causi belli, then use the monarch points and power projection to raise technology levels, and use money I received to build stuff and fund the colonization. There are some awesome dry land in the coast of California. After growing into a decent size,I got a subjugation mission on Pima. So I took the opportunity and annexed its ally Navajo too. It is like being flooded with monarch points when having high power projection, cheap advisers, 100 points in all three administrative, diplomatic, and military categories.
For those who wanted play more than just getting the achievement, you may colonize all around the Colorado and New Mexico regions. I’d suggest to reach level 3 diplomatic technology to get the settlement bonus too, it will be best if you can make exploration as your first idea group. Colonizing in the early game on arid land is not going to be fast. But one colonist only costs 2 ducats per month and it will be fast after escaping the arid desert.
In this game, Spain was mainly focused on the Caribbeans, Portugal was focused on Brazil, and France was focused on Colombia. England was merely starting to colonize Canada in the late 1500s. Small pox was ravaging on the new world and Feudalism is needed to cure smallpox, like that it is some type of vaccination. Native Tribes only can get Feudalism from nations that already have it, natives can’t make institution themselves. In my case, I could raise development in the Pima region, but then I don’t want to fight and core a 30+ development OPM with my low development provinces. Also, Feudalism is needed to reform religion too. I quit as this moment as I afraid I need to slowly colonize all the way to Florida to receive institution from the Spanish slowly. So I halted the plan of conquering the seven cities of EU4 institution.