You're almost at the end of the game.  The heating element is beyond the volcano at the farthest corner of the tropics.  You'll see a red pet.  He is extremely hard to charm.  I've played this game twice and found one of two things seem to work the best.  Chose a pet that has a high charm level or make your pet a color to increase his charming ability.  You have to click as fast as you can...lol.   one time my pet got extremely low and almost quit.  That's when I decided to make food before I went to charm him and feed my pet in the process.  Good luck.  You can keep playing after you finish the game but if you want to get all the metals before you end the game don't say good by to people. Have fun

There are 41 pets.  See the other answer for the names of the pets.  The first time I played I had the hardest time getting jimjim.  This time I'm having a problem getting imboko and murfee - I think when you get down to the last one or to the little guys just don't want to give up the eggs : )