Looks like there's a popularity contest going on, but the "Voting Tickets" have been stolen so we have to retrieve them. They even translated the cutscenes for this event.

->Open Spoiler<-

You'll need 2000 Voting Tickets to max out Lechenaultia and a total of 4000 for all the rewards.
All stages have a chance of spawning a bonus stage or raid boss.

?-3 - I went 2-0-1-2 with similar squad/helper speeds.
?-4 - Put 2 in the bottom right tent and a Lilac or fast squad at the top right one.

EDIT: You can view your ticket count at:

Originally Posted by fromelette

The vote menu is on the bottom banner ("popularity contest: polling booth") on the main page.

Don't forget to vote for your favourite girl!