The medium badge takes forever if you don't buy energy, ignore the gacha and spend the premium currency on energy and clear as many new levels as possible.
Levels like 4-3 make this a 1/5 for me though the other levels are really fun as it took me a ton of tries just hoping to get the things i need to actually win.
I got three stars on every level so i don't think it needs to be lowered, some do take five or six tries though as you need to click as soon as you can.
It's fun but the gap from level 12-15 is such a waste of time, you get 4 or 5 stars the first time you play each level then need to do it again constantly just to level up.
The only thing I ever spent money on was strong and with strong/special I managed to never have my book hit, it should be far more difficult as the shop is completely pointless as it is now.
That's when you use the nuke. ;D