One way we can see this in the novels/trilogy, is via his continued friendship and life long devotion to 'Strider' (Aragon); even knowing his dispossed status, he is willing to stand up for him at the Council of Elrond, when Boromir talks of him with contempt.
I just wanted to point out that where Legolas backs up Strider to Boromir only occurs in the film version by Peter Jackson. In the true "Council of Elrond" chapter in Lord of the Rings, Elrond actually tells Boromir that the ring cannot be used by man or elf, but only Sauron, the Deceiver.
In ''The Lord of the Rings'' trilogy, Legolas represents the Elvish strain of (a) noble courage and (b) integrity and loyalty; and we see him, time and again, risking his own life in battle and standing up for right and truth, against evil and duplicity and corruption.
A further example, is of his relationship with Gimli--elves and dwarves, as Prof Tolkien opined, didnt get along very well!--Yet, despite his 'natural' or even 'racial' antipathy to dwarves, Legolas has the moral courage to accept Gimli as a friend and admire (albeit grudgingly) his courage and prowess in battle, too, a number of times-- the Battle of Helm's Deep is probably the best example. This calls for great moral integrity.
Thirdly, is his volunteering to be part of the hazardous enterprise under taken by the Fellowship of the Ring, in going along as protectors and aides/helpers to Frodo, on his own highly perilous mission, in the face of heaviest odds and against all the worst forces of evil, as represented by Sauron and his cohort, the wizard Saruman. Almost all of the other members of the Fellowship waver at one time or th other--or are 'plunged' into some abyss or the other (as Gandalf is against the Balrog); or even for a time become tempted by the One Ring (like Boromir, leading to his death) and so on-- only Legolas remains firmly fixed on 'following' his 'mission' to the end, purely as an elvish warrior, and without greed or disloyalty. I guess this also calls for great moral/spiritual reserves,and this is precisely what Tolkien wanted to show and depict.
I hope this brief outline is helpful/useful. I am sorry I was not on enotes previously. Belated good luck.
Im also giving a couple of useful links, including one to the Official Tolkien Society,they have a fine library of material and lots of people/experts to help out on various Tolkien-related topics.