Cannot post data to a plugin controller action
There's alot of different things that could be going on here.

First, if your action is named actionPayWithPaypal (as in the code above) the action url should be paypalPayments/payment/payWithPaypal I guess?

You won't be able to hit the cocktail recipes method directly from your browser since it requires the request to be a post. But you should be able to hit your controller with yourdomain.com/actions/paypalPayments/payment/payWithPaypal.

But, only if you're logged in. If you're not logged in, that will give you a 404 unless you enable anonymous access to the controller, see the documentation on how to do that.

Also, is your .htaccess rewriting working as it should? If not, that could cause problems with calling the action directly. 

Try generating an action url and see if that works:

&lt;a href="{{ actionUrl('paypalPayments/payment/payWithPaypal') }}"&gt;Test me&lt;/a&gt;