Nymphs can be harmed much like any of their other "farie" kin... the problem is, Nymphs are typically evil and they tend to entrance mortals with their charms and use them for whatever purpose they wish... usually it ends in death.
Dragons, however, would have a certain immunity to the Nymph charm... so, I would qualify them to defeat a nymph... however, elves are also 90% impervious to various charm, sleep or hold spells... so no, Dragons are not the only creature that can injure a Nymph.
C