So uh, let me get this straight.
32000 points to get Blaze. Capped at 200 points per perfect battle. So, 160 wins.
Now, you get 1 orb per 20 minutes. there are 95 hours in the event. given that you start with 3 orbs and assuming perfect play, that would give you a total of 288 orbs to play with.
Assuming you get 6 hours unbroken sleep per day, that means you realistically have an approx total of 221 orbs to use.
Even given perfect play, you're still going to have to be hoving around your device for nearly 54 hours in order to get Blaze.
TL;DR - To stand a realistic chance of actually getting Blaze, you're going to have to use gems (assuming you can actually use them for this event of course)