Polishing will only temporarily solve your problem.
When recently polished brass is exposed to the elements, it starts to tarnish again.
After the brass has been reestablished, you would have to cover the surface with a spray lacquer sealant in order to keep tarnishing from again attacking the instrument.
Another issue is the amount of exposed brass the student will be in contact with. The exposed brass on the skin can be a health issue.
The cost of a complete refinishing will be more than the horn is worth.
Unless there is some sentimental value to the horn, it would be better to replace the instrument.