Alita from Battle Angel Alita (or Gally from Gunnm, if you prefer that)
Not only is Alita my favorite female protagonist, the manga is also my favorite manga ever (mind you, Last Order not so much, too much padding). Alita is strong, heroic and kind, but can also be vulnerable, pig-headed and cruel at times. Her main goal is to become the strongest fighter so she will no longer have to fight. Apart from being an awesome fighter, she's also well-read and has artistic talent (in her case music). And while she has a few love interests (and they are actually subject to change, their no one true love for Alita), she isn't defined by her romantic relationships alone, but also the father/daughter relationship she has with Ido or with the different friends she makes during the course of her story. Sex is also pretty much a non-issue here. Sure, Alita has a clearly female body, but it's all metal with no genitalia. Throughout the story manages to gain the respect and adoration of many people, allies and enemies alike, through sheer will-power and awesome-ness.
All the days are here: Day One: Favorite lead female character Day Two: Favorite supporting female character Day Three: A female character you hated but grew to love Day Four: A female character you relate to Day Five: Favorite female character on a male-driven show Day Six: Favorite female-driven show Day Seven: A female character that needs more screen time Day Eight: Favorite female character in a comedy show Day Nine: Favorite female character in a drama show Day Ten: Favorite female character in a scifi/supernatural show Day Eleven: Favorite female character in a children’s show Day Twelve: Favorite female character in a movie Day Thirteen: Favorite female character in a book Day Fourteen: Favorite older female character Day Fifteen: Favorite female character growth arc Day Sixteen: Favorite mother character Day Seventeen: Favorite warrior female character Day Eighteen: Favorite non-warrior female character Day Nineteen: Favorite non-human female character Day Twenty: Favorite female antagonist Day Twenty-One: Favorite female character screwed over by canon Day Twenty-Two: Favorite female character you love but everyone else hates Day Twenty-Three: Favorite female platonic relationship Day Twenty-Four: Favorite female romantic relationship Day Twenty-Five: Favorite mother/daughter and/or sister relationship Day Twenty-Six: Favorite classical female character (from pre-20th century literature or mythology or the like) Day Twenty-Seven: A female character you have extensive personal canon for Day Twenty-Eight: Favorite female writer (television, books, movies, etc.) Day Twenty-Nine: A female-centric fic rec Day Thirty: Whatever you'd like!