What is Boxer trying to achieve in Animal Farm?
Part of what makes Boxer such an honorable and decent character is that he really does not have anything resembling a personal agenda. In his characterization, he is not trying to achieve anything directly self- serving. Boxer lacks any personal motivation or drive for his own goals and his own desires. His selflessness, willingness to sacrifice for others and make others' goals realized represents the crux of what he is trying to achieve in the narrative.
This is what makes his so susceptible to manipulation. He is persuaded by Animalism, and is swayed towards revolution. Boxer's admiration from the other animals comes from his willingness to do for others. Boxer tries to achieve the realization of their goals. When the farm needs more work from its animals, Boxer exceeds the already high expectations placed upon his work output. When the farm needs him to sacrifice, he willingly does so. Boxer is only trying to achieve what others want from him. This is what ends up killing him, as he becomes too old to work at such a high output and level. In the end, Boxer has no real personal wants and no sense of personal desire. There is nothing that he, himself, wants. While he is dying of his collapsed lung, Boxer reveals that he is trying to achieve retirement and learning "the rest of the alphabet." This is the closest he comes to trying to achieve something for himself, a desire that ends up being muted by the machinations of the pigs.