I have a suggestion for bathing cats and dogs which has worked extremely well for me for many, many years. This only works if you have a stall shower with sliding doors - a curtain will not work. You also need a hand held shower head.
First I strip down to undies so I don't get my clothes wet. Then I pick up the animal, get in the shower, and close the door. Put the animal down and let it walk around. Start running room temperature water. Spray the animal. Avoid getting their heads wet. I wash faces/ears/heads with a damp washcloth. This approach will not
work if you start by spraying the poor critter in the face.
Get animal wet. Start lathering with the neck in case there are fleas. You don't want them to migrate from the body to the pet's head. Then lather up the rest of the animal. If using flea shampoo or medicated shampoo, turn the water off while the shampoo sits for 5 minutes. During the waiting period, whisper sweet nothings to your little one while massaging them. The late Bootsie (a cat) would actually purr during this part because it was the only time Midnight let her have my undivided attention.
Finally, rinse, rinse, and rinse again. Shampoo/soap left may irritate their skin. I dry with a towel. Whisper more sweet nothings while drying.
We've had Honey Girl for 8 months and she gets bathed weekly. She started out quivering the whole time and now it doesn't bother her a bit. When summer comes and we have a hot day, I'll give her a cool shower and she'll be a convert. My old dog, GingerBear, would beg for showers on hot days. On the other hand, the cat, Buddy, may never agree that he needs bathing, but using the above approach, he takes his frustrations out on the sliding glass shower door and I emerge scratch-free!