Took some liberties with normal types here. No such thing as a "normal" boss battle so I am working on animal based boss battles... ironically I couldn't find that many of them that I could also call normal so I cheated a little. Enjoy the list.
FORMER LISTS
WARNING possible Spoilers WARNING
Remember I said possibly cheating? This fight is incredibly low because I honestly don't know if this counts. Really this little beast... he'd be a normal pokemon right? I'm not sure. Anyway, the fight is actually pretty fun and I do like the creature's design and place in the story, but it isn't the greatest boss either and can be annoying to deal with sometimes.
Lame boss fight, not really memorable, but they are animals unlike Cerberus. These are pretty easy boss fights but it does slowly get better from here.
Slowly. Conga is a large gorilla who gives you trouble in the first level of the first game. He throws oranges, and you get to shoot eggs at him. Nothing to right home about but it does give you a chance to try out shooting eggs.
When I first played this game this boss took me a while to figure out. It is a large teddy bear with a ghost mouse controlling it, and you basically have to lower it to smack it around and hit the mouse. While a little whimsical, this fight can be really fun, but fairly easy once you get use to it.
While her symbiote fight is harder, her original fight is probably more fun as she flirts with you and even will kiss you mid attack. It is probably the strangest thing ever except maybe a giant battle cake, but it left an impression for sure. The fight can actually be challenging as well, while the symbiote fight with her can get annoying due to Mary Jane.
Since Clefairy is now fairy type, I think this is more for Whitney's Miltank then Whitney herself. If you are unprepared that dang cow will trample you (erm rollout) into the ground. That being said, there are a few ways to deal with Whitney to not make her all that difficult. First off you can trade a Drowzee for a Machop and use the Machop to destroy her. That or train a pokemon resistant to rock attacks. Either or I thought she was a fun fight.
This guy isn't on the fighter list coming up!? Must be an April Fools Joke right? Well he is animal based and there is a reason for this. Rawk Hawk is a fun boss fight and is a silly but cool character in the game. Heck he isn't even the main third boss but dang if he didn't just end up being the most popular boss fight of all time from Paper Mario... maybe. He also cheats. Still a fun boss fight for sure and a great character all around.
Snakes are normally poison types so this is a stretch. No poison attacks though so works in my book. the Egg Viper is a powerful robotic machine that you fight in Sonic Adventure as Sonic's final boss fight. This fight is incredibly challenging and really fun to fight as the thing uses so many tactics to destroy you. It is ultimately satisfying to beat Dr. Eggman here.
Fire Normal type? Does use double team... wait that isn't a pokemon it is Bowser in a cat suit. Silly me. While not actually much of a boss fight, hence why it is number 2, it is still a great scene with a "boss" so there you go. Cat Bowser is incredibly creative as a final fight, as he climbs the skyscraper you are on and tries to claw and use his tail to attack you. Then he grabs a double cherry... or a few of them... and then you are climbing the top of the tower with five cat bowers trying to destroy you. It is intense, fun, and dang it may never leave my memory any time soon.
In Donkey Kong Country at the end there is the king of the crocs, King K. Rool himself. At first he throws his crown a few times, you stomp on his head, his cape is poison as I put it in my youth, and he dies, credits roll, I love the fight because easy is my game that is a wrap goodnight folks... of course I'm kidding this was written on April 1st after all. After a few credits roll, K. Rool decides he was only winded and gets up. He begins jumping around the stage instead of running, and using a smash ball.... (jk) he begins summoning cannonballs from the sky to fly down and smash Donkey and Diddy. These cannonballs are huge, and very deadly. It was a tough fight, heck, still is a bit tough, but I made it through as a kid. As animal boss fights go, this is my personal number 1. Thanks everyone, happy April Fools Day.