How to install sink drain pipe correctly
I've had similar problems sometimes with sink drains. I'm guessing it's leaking were the rubber washer and the sink bottom connect? If so: 


Make sure the black washer is fitting correctly. It should almost fit into the opening, but still have part of the curved section showing. Tightening the plastic nut will force more of the round section further and tighter into the sink bottom. 
Check the sink drain opening for any irregularities. Run a finger tip around the drain edge and feel for bumps; it should be perfectly smooth. 


I'm guessing the clicking sound you heard may be a stripped thread on the drain or a cracked nut. The PVC plastic is very easily cross threaded if not lined up correctly. Sometimes you can "uncross" the threads with a sharp utility knife. 

If the two suggestions I first mentioned don't apply and nothing is working it might be worth noting that the type of drain in your photo (the accordion or flexible-type) is not up to code anymore. It may be easier to purchase a new rigid P Trap.