Star #1 = Just clear the stage
Star #2 = No damage
Star #3 = Never have more than 30 active units during the battle
Crown = All star conditions (#1 + #2 + #3) at the same time
Star condition #1 and #2 are very straightforward, but you need to pay attention a bit more to fulfill the condition #3.
You can find a chunk of numbers at the bottom left corner of the screen.
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Active unit count / Deploy limit (Always 40)
Max deployed count
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In order to get the Star #3, you must keep the "Max" value lower or equal to 30 until the end of the battle.
I hope this post can help someone understand the concept :)