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If it clearly shows someone lunging at you then it shouldn't need enhancing.
Firstly if you are worried about admissibility of this footage then getting a random person on the internet to edit it for you would be the fastest way I could think of to get the footage kicked from the case altogether.
CCTV enhancement is a fairly specialized field so if you are facing criminal charges I would highly recommend engaging someone qualified in the field to undertake the work for you, this way you are much more likely to have the evidence admitted in court.
Lastly, if there is CCTV footage of the incident then I'm fairly certain the Police will already have it and will have engaged their own experts to clean the footage up. I'm not sure about the US but in Australia under discovery laws the Police have to make any such evidence available to the accused prior to the trial. So you may well be entitled to an already enhanced copy of the video courtesy of the Police and at no cost to you.
Edit out of curiosity I downloaded the file (1 GB) and had a look at the video. There are some issues with the quality, firstly every 20 seconds or so the screen goes entirely black and seem to maybe skip a fraction of a second. Secondly, I'm assuming all the action happened at the far end of the alley way because as soon as you guys step into the sunny area you can't see jack diddly.
The footage at 10.25 you can see something happen, but just before it happens the footage changes camera for a split second and then back and you can see her move suddenly, but to be honest I couldn't tell if she was pushed or she was doing the pushing. I watched it a dozen times and had a few colleagues take a peek too. General consensus is that no one could tell what happened, too far away to really see.
You need to get an expert to look at the original footage but I suspect little could be done with it.