To cultivate something is to tend to it and help it flourish. This verb is widely used to talk about tilling fields and growing crops. However, as a synonym for the more general verb develop, cultivate veers into metaphorical gardens: when we cultivate talents or skills, we refine them, perhaps with lessons or practice; when we cultivate relationships or friendships, we encourage and promote them; and when a celebrity cultivates an image, they are carefully crafting a public persona.
A goal is an achievement toward which effort is directed, such as getting into a certain college or running a marathon. An intention is what one means or hopes to accomplish or carry out. It is close to a plan, emphasizing what is held the mind as motivation or purpose. Sometimes, however, the word is meant to highlight distance between what is planned or wished for and what is put into action, as in the case of good intentions that fall short of producing an outcome.
To strive is to exert oneself vigorously or to try hard. When we strive for something, such as excellence or success, we are making strenuous efforts toward that goal. This verb emphasizes a tireless determination; after all, excellence and success are not easily attained. It also suggests a degree of strife, reflecting earlier, more outwardly oppositional uses of strive to mean “to rival,” “to compete,” and “to struggle vigorously, as in opposition or battle.”