I hate it say this but it seems that you have already diagnosed your problem - horrible lighting.
You are either stuck with what you have or you would need to reshoot the green screen shots. In short, bad green screen results in bad keying and that's pretty much that. You can minimize it the best you can by fiddling with brightness/contrast but in the end, it is what it is.
I'd suggest that if it isn't too difficult, properly light your green screen and give it a second try.
PS: There are many other things that prevent this from looking professional as well so I have to assume this is mostly for fun but the perspective is quite a bit off with the placement of the guy. I don't want to beat up your work but just pointing out there are a number of things that could be improved, the green screen being the obvious one.
I agree with kirkeric's comments. You need to re-shoot to fix the chroma key and to fix composition problems.
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I would guess that you shot this with an amateur camera and the footage is highly compressed. The color is probably 4:2:0, and if you under expose or poorly light highly compressed footage it's going to be very difficult to produce a clean key. A lot can be done with the settings to improve your key. If you used Keylight you have a lot of options. I would suggest that you try and save as much as you can by first, selecting the layer and then pressing the U key twice. This will show you everything that you modified. If there are only 3 or 4 settings that show up then explore some of the other options.
To learn how to monkey with the controls type the name of the keying effect you used in the search help field at the top right corner of AE and study the help files and look for tutorials from instructors that know what they are doing. Most of the YouTube keying tutorials you find with a Google search are by amateurs that don't really know what they are doing or how to solve hard problems.
If you are completely lost then show us the complete comp with the modified properties of the keyed layer revealed by using Print Screen and then paste to this forum. If you are using a Mac press Shift + Ctrl/Cmnd + 3 and drag the screenshot from the desktop to the reply field on the forum. Maybe we can help.
Thank you for your comments Dave and kickerick. I have done some videos in order to learn the program hoping I could do it professionally at some point...!!! But probably I have a long way to achieve that....
Rick I will do what you instructed me! Thank you too!!