It looks like that Tetra may have been in bad shape for a while, honestly don't know how much he can recover now, but yes, do more WC then usual. At least in the beginning. If he does not improve much, just keep him healthy.
That is one VERY unhealthy tetra and it looks like it is nearing the end of its life. The best thing to do is to keep him healthy. If you figure out what he is then get more of him and he may be happier.
Just a little update. I bought 4 more Rosy tetras, and this old tetra seems to be a LOT more happy! Seeing them all together looks so nice, and you can really tell that my tetra is actually a rosy tetra. So I'm happy that all has ended well. All the fish seem to be getting much better. Can't say too much about the fins, I'm sure those take longer to heal than the fish's activity level (I had dealt with a betta that got fin rot from ick and lost almost all his fins and was on the verge of death. He got better quick, but his fins took longer to grow back.)