context: The year is 1966. Saya is the only remaining original
  vampire, and she hunts Chiropterrans--demons who live off human blood.
  Saya's a testy and demanding little bitch but apparently very valuable to
  "the top." Her next assignment, as her boss David explains it to her, is
  to infiltrate the U.S. Yokota Air Base's High School, which has been the
  scene of several deaths in the past and is thought to be harboring at
  least two Chiropterrans. Saya's cover is that of a student who will be
  participating in classes for a few days.Saya's first day at Yokota High is pretty uneventful. After classes
  are over and everyone has cleared out, Saya snoops around the school and
  learns that blood has been spilled on the floor in the infirmary. She
  suspects that the infirmary is the Chiropterrans' feeding room. The next
  day is the school's Halloween party. After school lets out, the students
  change into their costumes and head for the dance...all except for Sharon
  and Linda, that is. Linda isn't feeling well, and Sharon thinks it's a
  flare-up of Linda's anemia, so she's going to walk Linda over to the
  infirmary and they will attend the party later. Saya enters the infirmary
  just as Sharon and Linda are about to feed on nurse Makiho Amano. Linda
  changes her form into Chiropterran, and Saya slays her with her sword.
  Saya turns on Sharon and wounds her, but Sharon gets away, spilling blood
  as she flees. The astonished nurse follows the trail, which leads to the
  dance hall where she finds Sharon in Chiropterran form hiding under a
  blanket. While Saya battles the creature, Makiho runs for help.Meanwhile, at a nearby bar, the mama-san sets the bar on fire, takes
  Chiropterran form, and heads for the army base. She kills the military
  guard who is escorting the Makiho back to the dance. Saya saves the
  terrified nurse, and they take refuge in a military garage, but the demon
  finds them. Saya, without her sword, battles the creature with a shovel
  while Makiho hops in a jeep and rams through the door. David, who has been
  looking for Saya and was standing outside the garage, tosses a sword to
  Saya, and she chops the demon (Sharon) in half. As Saya and David take
  Makiho from the jeep and lay her unconscious form gently in the grass, they see the mama-san in demon form on the roof, preparing to fly away.
  David and Saya follow in the jeep. The Chiropterran tries to escape by landing
  on the wing of a military jet tooling down the runway. The jeep gives chase,
  and Saya slays the monster. As the Chiropterran lies dying on the runway,
  Saya feeds it with a few drops of her own blood.Epilogue: Makiho attempts to describe what she saw to the military brass, but
  she has little proof of anything. When she returned to the infirmary,
  Linda's body was no longer there and the bloody mess had been cleaned up.
  The military brass deny knowing anything about David, but they do show
  Makiho a photo taken in 1892 that clearly shows Saya and has the word
  "Vampire" written on it. Makiho returns to her office, wondering to
  herself whether Saya is still around and still fighting demons, "just as
  we humans continue to kill each other." At that moment, an announcement
  comes over the radio that the Liberation Front has attacked the American
  Blake base and that Yokota base personnel have been ordered to fly to Don
  Hoi in North Vietnam. As the credits roll, the background shows some very
  blurry photos of what looks like American forces in Vietnam.
  [Original Synopsis by bj_kuehl] [Edited by m-lissa1]
question: What has Saya been obsessed with doing?
answer: rid the world of vampires