Catwoman is the only blaster with a melee basic attack, making her more vulnerable during laning, and her scaling is somewhat lower than other blasters. However, she can deal great amounts of consistent damage over a moderate duration with Bad Kitty (faster than Star Sapphire but slower than Stargirl). Most of the damage, however, would require her to be very close to her target. On the other hand, with Bad Kitty, Acrobat/Savage Acrobat can be used six times in a row, making it very difficult to catch or escape from her.
Because of her melee basic attacks, consider last hitting drones with Whip Strike as much as possible. It deals bonus damage at the edge of the skill range, and has a low Will cost.
The coin created by Cat Burglar always flies from the target towards Catwoman's general direction; while it can land to the side considerably, it always lands roughly as far from the target as Whip Strike's maximum range, further encouraging Catwoman to keep her distance in lane. Also, try not to last hit drones backwards (e.g. last hitting a melee drone that is attacking your turret with a basic attack while standing slightly further away from the turret), as this would cause the coin to fly towards the enemy side.
Acrobat -> Whip Strike on a group of drones can allow you to use Acrobat again much quicker for chasing or escaping, due to the cooldown reduction of Cat Burglar.
Bad Kitty's cooldown can be deceptively low in later stages of the game as Cat Burglar can shave off a sizeable portion of the cooldown over time when pushing a lane.
Remember that Bad Kitty also resets Acrobat's cooldown, so use Acrobat immediately before Bad Kitty.
Savage Acrobat offers the same empowerment like the regular Acrobat. The empowerment from Acrobat or Savage Acrobat does not stack: make sure to weave in a Whip Strike or a Cat's Paw in between Acrobats to make full use of it. Whip Strike offers decent area damage over time, and its cooldown is very short, almost as short as Savage Acrobat; you could also use Cat's Paw to knock down priority targets once during her ultimate.
While Bad Kitty is active, all targets struck by the Acrobat-empowered area of effect Whip Strike will suffer from bleeding damage.
Catwoman's only interrupting crowd control comes from an Acrobat-empowered Cat's Paw and a lot of her damage comes from Savage Acrobat. Be careful when dueling the likes of Stargirl, whose ultimate, Energy Conversion, cripples her target, preventing Catwoman from using Acrobat and therefore unable to interrupt or escape.