There are many options for tutoring, but one of the best is the one you have somewhat discounted already: upperclass.
The benefit of the upperclassman is that you can find one/many who have had that professor before and know how the tests go. They can be a treasure trove of information and it is expected that you seek out successful upperclassmen if you are struggling.
Other options in the past have included a tutor that was brought in by the Academy; however, budget cuts and other causes have since seen that disappear.
You can bring in your own tutors from the outside if you so desire. The Academy is an "open" campus meaning they could meet them in several locations for help; however, the cost would be on the midshipman/parents.
The ACE has in the past had help available.
Also, usually the professors have office hours or the department does at which midshipmen can seek help. The caveat I give here is that if you don't feel like you are learning well from a particular teacher simply spending more time with that person isn't necessarily going to give you any progress. Potentially I would recommend seeking out one of the other professors in the same dept to see if you can get a different angle.
Oh, almost forgot: don't forget to speak with the Company Academic Officer. They usually know what resources are available.