-( Story related, cannot be missed )-
Despite the description, you don't have to actually fight him with your fists. I finished the fight using the EZ Gun in Very Easy. The only flaw with using a gun in general in thsi fight is that, most times, he'll end up actually deflecting the bullet. This isn't to say that it is impossible, just challenging to find the openings.
One opening comes from when he's spent from using his electrical attacks and runs over to a fuse box to charge up. You can get a few shots in at this time. Another opening, albeit brief, comes from after he charges up and does a left-right blast of bullets trailing after you. You could also try to get close and do some CQC (since it's suggested) or use the Handkerchief against him, but personally I didn't try.
Do keep in mind that this is a two-stage fight dividing his stamina. You are also timed in the background over the discovery of the C3 charges and the timer placed on them.
If there is anything more to add to this, or alternate ways to deal with this boss, please let me know and I will add it and credit you. Please let me know what I can do to help further if you choose to down-vote this solution.