You can exit out of a puzzle map at any time by pressing "k". Some puzzle maps are quite hard. There are multiple solutions available, but I can offer some hints for good opening moves:
Sneaky bats: Try opening with a sleep spell aimed at the top group and changing the directions of the two bottom bats.
Armored Spiral: Swap with Ebrem, send the bat and slime that are approaching Fei to the top, walk outwards along the spiral to regroup.
Tower Defense: Send Kobu along the path down, then Fei into a counterclockwise loop. Clearing the first group of 4 mice is very important, keep Kobu on the rightmost edge to hit multiple ones.
Island Hopping: Swap with the mouse mage using a sleep spell. Follow grey mouse until it's lined up with the snail and swap using reflection spell. Shoot the snail with a direction swap spell to bounce it at Ebrem to rescue him. Remove shield from grey mouse using healing spell and rotate it around on your next turn. Heal Fei and make her face top to swap with the mouse mage. Rotate slime sentinel to help Ebrem defeat it. Help Fei defeat the grey mouse at the top. Bring Ebrem to the central island to defeat the mice there (Fei has a tough time because of her spell). Clean up using Fei.
Medical Crisis: Send Kobu down, move down and support her with a strong healing spell. Move right and turn the bat left to save Fei. Turn Ebrem to move to the top. Send Fei to sustain Sophie until you can send Kobu down to shoot the slime.
Waiting for Kobu: Turn the snail around when it comes close to keep it out of the way. Turn Sophie right, and support her as you make your way right. Make Kobu go back as soon as she's in range. Use your extra spells to get Sophie out of any bad situations that arise and try to clear some of the enemies (with good timing and planning, only the mouse mage and snail will remain by the time Kobu comes).
Surrounded: Turn Fei left. Put a ward on Kobu. Charm the top slime. Turn the snail around. Turn the charmed slime right. Make your way towards Sophie, turn Kobu and Sophie away from the enemies they're fighting. Cleanup shouldn't be too hard after this opener.
Around the Loop: Turn Sophie towards you, follow Kobu. Swap with Kobu and turn the slime sentinel around. Move to the top-left corner of the lake, let Sophie fight until a 2 tile gap forms between you and Kobu. Swap with Kobu. Support Sophie with healing, turn Kobu to fight the bat, turn Sophie around after the bat bishop is defeated and regroup. Keep Kobu from running away on her own, and you should be in good shape for an easy cleanup.