“Come on! You've got to at least give it a shot.”

There's an art competition that you were thinking about entering, but now you're thinking you won't enter it because you don't have a chance of winning. You tell your friend that you're not going to enter, but she disagrees. She says:

Come on! You've got to at least give it a shot.

come on

You say "come on" to someone when you're trying to convince them in a friendly and casual situation. "Come on" means something like "Don't worry about it; just do it." Here is another example:

Come on! Tell me what she said!

Come on, stay for one more round.

You've got to (do something)

When speaking with friends and family, you can encourage them to try something by saying "You've got to ___!" For example:

You've got to try this sauce. It's amazing!

I had a great time. You've got to go with me next time.

at least (do something)

When you want someone to do a something, but they don't want to do it, you state a lower minimum amount that you think they should do using "at least ___":

You can at least take out the garbage, since I cooked and washed all the dishes for you.

He could at least say "hi" or something.

give it a shot

"Give it a shot" means "try it". It's a more casual phrase than "try it", so it's good for conversations with friends and family.