Isn't it ridiculous that I'm 35 and I still get scared to show my dad my new tattoos.
Why are you worried about showing him the tattoos?  You're a grown man!
I feel like he will not like them
You're an adult now and should feel free to take whatever actions you wish. Don't be ashamed to share them with your father, there's nothing wrong with what you did!
Fuck man I don't know what to do. A week ago, I showed him a photo of the tattoos and he said he didn't like the snakes. I didn't expect to get that reaction from him.
Maybe he doesn't mind tattoos, but he didn't like that design. Try being honest with him about your tattoos. He might surprise you.