Galadriel's powers mainly lay in the areas of defense and being able to see into others' minds. She learned a lot from Melian the Maia, during her stay in Doriath in the First Age, so the "girdle" around Lothlorien could have been partly derived from the Girdle of Melian around Doriath. She and her people managed to repel three attacks from Dol Guldur, so we know that Lothlorien was a rather strong principality.
Her ability to "use" the Mirror probably lay partly in her mental strength. I believe that it says in The Silmarillion that she was always good at searching the minds of others, but that she never used it to judge them unfairly or harshly.
I can't think of any other "powers" that Galadriel might have.
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But Melkor also was there, and he came to the house of Fëanor, and there he slew Finwë King of the Noldor before his doors, and spilled the first blood in the Blessed Realm; for Finwë alone had not fled from the horror of the Dark.
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