You can press surrender and try again when you lose most of your good monsters but sometimes this can prevent you from getting some really cool monsters in the shop. Certain monsters are unlocked by not surrendering or losing in a specific area. Below is a complete evolution list.

Dark Witch - Lv. 4 LaMoon / 50 light square
Fireyarou - Lv. 3 Flame Manipulator
Great Moth - Lv. 3 Larvae Moth / 30 wood square
High Tide Gyoj/ - Lv. 6 Root Water / 50 water square
Hunter Spider - Lv.4 Kumootoku
Hysoube - Lv. 6 Psychic Kappa / 50 water square
Larvae Moth - Lv. 3 Petit Moth / 30 wood square (I wouldn't Petit ;-D
Magician of Black Chaos - Lv. 4 Dark Magician / 40 dark square
Manga Ryu Ran - Lv. 2 Ryu Ran
Mon Larvas - Lv. 4 Larvas
Pengu/ Knight - Lv. 3 pengu/ Soldier / 40 water square
Red Eyes Black Metal Dragon - Lv. 4 Red Eyes Black Dragon / 60 dark square
Rock Spirit - Lv. 5 Haniwa / 40 earth square
Ryu Kish/ Powered - Lv. 5 Ryu Kish/
Sh//g Friendship - Lv. 5 Petit Angel
Trent - Lv. 4 Ancient Tree of Enlightment
Tripwire Beast - Lv. 6 Electric Lizard