How do I get the pixel sprays for each character?

Each character has two achievements. The "Cute" sprays are generally (but not universally) tied to skillful use of ultimate abilities, while the "Pixel" sprays are tied to more general use of the character. Specifically, the Pixel sprays are rewarded for:

Ana: Interrupt an enemy's ultimate ability using a Sleep Dart.

Ashe: Kill an enemy by shooting Ashe's dynamite from at least 30 meters away

Bastion: Get a total of 2 eliminations while in each of Recon mode, Sentry mode, and Tank mode in a single life (the Tank kills do not have to be in the same use of the ultimate)

Brigitte: Interrupt an enemy's ultimate ability with Brigitte's "Shield Bash"

Doomfist: Get a killing blow with Doomfist's Full Power Seismic Slam.

D.Va: Block 1500 damage with a single use of Defense Matrix

Genji: Kill 2 enemies with a single activation of Deflection

Hanzo: Get 3 killing blows with a single use of Storm Arrow.

Hammond: Absorb 1500 damage with Wrecking Ball's "Adaptive Shield" without dying

Junkrat: Use Concussion Mine to knock an enemy into your Steel Trap

Lúcio: Get 3 killing blows while wall-riding in a single life

McCree: Interrupt an enemy ultimate with Flashbang. (Not all ultimates can be interrupted)

Mei: Block 1200 damage with a single use of Ice Block

Mercy: Heal at least 200 damage on each of your five allies in a single life

Moira: Fully deplete both types of Moira's Biotic Orb without dying.

Orissa: Pull enemies into 1000 damage with a single use of Orissa's "Halt" ability

Pharah: Push someone to their death off a cliff using Concussive Blast

Reaper: Kill 3 enemies in a single clip (that is, without reloading. You can use Death Blossom to soften them up, but the killing blows have to be with your primary fire)

Reinhardt: Block 8000 damage with Barrier Field in a single life

Roadhog: Interrupt an enemy ultimate with Chain Hook

Soldier 76: Get 2 killing blows with a single use of Helix Rockets

Sombra: Hack 15 players in a single life.

Symmetra: Hit an enemy with 3 beams at once (two of your sentries, plus your primary fire)

Torbjörn: Absorb 500 armor damage with Torbjörn's Overload without dying.

Tracer: Recover a total of 400 health with Recall in a single life

Widowmaker: Get 4 kills with Venom Mines in a single match (You can soften an enemy with your rifle after they have triggered it, as long as the damage-over-time from the Mine gets the killing blow)

Winston: Destroy a total of 10 turrets (Torbjörn's or Symmetra's) and/or mines (Widomaker's or Junkrat's) using your Tesla Cannon in a single life

Zarya: Maintain 70% Energy or more for 60 seconds

Zenyatta: Get 4 assists or eliminations within 6 seconds using Orb of Discord