Requirement of the “A Sun God” achievement requires having core/colony of all South American provinces as Westernized Inca. Well, how can you even survive without westernizing anyway? This will be my progress, or guide of getting this achievement. I started as Cusco, the strongest Incan nation at the moment with a leader with awesome stats.
I chose Exploration, Defensive, Religion, Expansion, Offensive, Trade idea groups. I still haven’t choose the eighth one yet but the first three is very important because the first two allow you to explore and expand territories around the your empire, one to boarder with European colonists, second to expand, and thirdly, you can afford the colonists. You will need extra morale and army tradition to fight off Europeans if they are going to attack, it is very likely especially before finished westernizing. I think Quality may work as well because it gives combat bonus. After reforming your religion, you will have some bonus and raised your admin, diplo, and mil technology level into 8, by that time you can unlock two idea groups and choose some idea with extra points.
And this is the easy part, uniting the Incan tribes. This is relatively easy comparing to the next step. You will collapse, like the Inca in history if you done the second part (reformation) wrong.