Arwen, on the whole, is a gentle and loving soul, slightly playful. There are four traits in Arwen's personality that shine above all others:
Arwen is faithful. She worked ceaselessly on her banner for Aragorn and watched over him constantly in thought. Not once did her faith waiver; not in Aragorn, her future, or in herself.
Never a more selfless woman has lived. She loved Aragorn so much she gave up her immortality. In doing that, she gave up her father, the chance to see her mother again, her people, everything she knew and treasured. For love alone. And not only that, she gave up her position on that ship across the Sundering Seas to Frodo. Could you be able to do that? I wouldn't. Which brings us to another point...
Arwen knows true courage - my goodness, does she ever! She had the bravery to willingly walk into almost instant death: remember, she is over 3,000 years old. The sixty years she ruled with Aragorn must have seemed like a heartbeat to her...
The trait of an elf, or a woman, or both? Frodo never spoke of his suffering, only in moments of intense suffering, and yet Arwen could see that he was in a lot of pain, and gave up her position in Valinor for him without a qualm.