Looks like I figured out why my car doesn't like starting. Do you think I can repair this by replacing the terminal or I need a whole new negative cable? 
Discussion
If you have enough slack in the cable to still reach after, I'd cut and recrimp the negative lead
Shortening the cable and re-crimping it might be the quickest solution, you can also try removing the oxidation on the cable first to see if that fixes it, that green part might be stopping the conduction
Depends on a few things.
1. How far back does the damage go. (You'll have to open the harness and find out where the cable is still flexible by hand. A visual inspection won't be enough)
2. Is there enough slack in the cable to reach. (After performing step 1)
There are splice cables and terminal assemblies available if it doesn't reach.
Using a design that solders to the existing cable is preferable, but crimping and using marine grade shrink tubing is second best.