I had a child like this, it's VERY tough as they are simply not as easily manipulated or motivated as more easygoing kids! I used to cry at how little pleasure I got from my own child.
Assuming she's definitely NT (I'm sure there will be other approaches if not) my advice is:
Set clear visual parameters in advance. So you play with her, but before you start you tell her that "when this hand gets to X" on the clock it's time to stop. Same applies if you need her to wait.
What is her driver/"reward"? With my son it was food. Clear warning - "do X again and you'll have no pudding", and follow through. It was a real motivator. If your DDs is play, then say you won't play with her the rest of the day.
Temper tantrums, I would shut down immediately and take kid straight to their room, no debate. They can scream and dick about but you don't need to listen to it.
You explain that when she's ready to be quiet she can come out. If she's there ages so be it. At 4 she knows how to get herself released. My son soon stopped the tantrum as soon as he started up the stairs!
For something truly defiant and naughty, bin a favoured toy. Just do it and let them think it's gone. You can always retrieve and hide it away for a future date (not too close) and make out you've bought another as a reward for being good.
Praise is the HUGE one. In the well-behaved moments where you're actually less aware of her, remember to praise her and really gush. She wants a reaction as you said - give her the reaction when she's being GOOD. Take her to the cupboard and say "you've been playing so quietly for mummy you may choose a little treat". Surprise her with the odd toy after work. Suggest an extra game or bedtime story. Never as a bribe, only as a proactive response to good behavior. She will learn that she gets more from mummy by being good.
It's never as easy as it looks on paper and god knows their will is strong! Just always remember you are the parent, you have the power - treat her with kindness and affection most of the time so she's never in any doubt of your love - but don't be afraid to be harsh. Your daughter will get the best of YOU in the long run and be happier for it.
FWIW my child was a little devil for about 6 months but the above really made a difference. He still has the strong temperament (no bad thing!) but is very well behaved now.