The best example of a cultural achievement of the Portuguese maritime empire from the options provided is:
B. the Portuguese spread Christianity with great success, winning over the favor of rulers in China.
This highlights the cultural aspect of the empire, specifically the dissemination of Christianity and the establishment of relationships with local rulers, which reflects the cultural and religious influence the Portuguese aimed to exert during their maritime explorations and expansion.
Options A and D relate more to military and economic control, while option C pertains primarily to agricultural changes resulting from trade rather than a direct cultural achievement.