Pretty hard to say from the photos, but growing tips going fast like that kind of rules out early blight (which usually starts low and works up). I am not sure but suspect late blight might well be your issue; it certainly looks and sounds fungal, and this can be a worst case scenario. I suspect you are not out much dough on a plant this size and might even consider a new start, but if that's not an option you have a few others.
I'd first try a mild H2O2 treatment; four ounces of 3% hydrogen peroxide mixed with a gallon of water and spray top to bottom, saturating everything. This is a good antimicrobal for fungus or bacterial, so in the off chance it is a bacerial leaf spot we have covered that angle as well.
Now that we have decreased the biology in the phyllosphere (fancy talk for killing all the critters and mushrooms on the leaf), we need to put some back. Just like any ecosystem on Earth, healthy biodiversity is the key to not letting any one species dominate the system (like some nasty blight on your maters). We can put it back a lot of ways but milk does this easily, cheaply, and I know what the answer is for most folks if I ask "got milk?"
10:1 is a good preventative mix but I go 3:1 water to milk for existing disease, spray to saturation, and repeat. Millk has some [url=https://www.raw-milk-facts.com/lactoferrin_T3.html]amazing chemical properties[/url]of its own ([url=https://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6T99-47243N5-3&_user=10&_coverDate=05%2F12%2F2000&_rdoc=1&_fmt=high&_orig=search&_sort=d&_docanchor=&view=c&_searchStrId=1243025508&_rerunOrigin=google&_acct=C000050221&_version=1&_urlVersion=0&_userid=10&md5=ad02113b980210bb88415c0740c92f1a]goats milk too[/url]), as well as being a preferred growing habitat for Lactobacillus, the world's most common and useful bacteria (we use it not just a a composter, but as the catalyst for sour cream, cheese, yogurt, kefir, kim chee, saurkraut, pickles, sourdough bread, Belgium lamberts (mmm, Belgian lamberts...
). It is a discriminate and mostly benign, even beneficial decomposer, as it seems to be [url=https://www.treesearch.fs.fed.us/pubs/21594]antifungal in it's own right[/url]. Heck, [url=https://www.ingentaconnect.com/content/ocean/aap/2006/00000027/00000005/art00015]milk is how we get antifungal[/url]
Fish hydrolysate (a purified emulsion) is another good way to stimulate biologies; the day after I did the milk I might follow up with this. As directed on the bottle, this is a good bacterial food and a good fungal food but we have already tipped the scales to bacterial with the milk spray and the nitrogen in the fish spikes growth in our Lactobacillus even further. Our leaf is now again protected from further infection by a film of antifungal milk populated by antifungal bacteria. Take that fungus.
Or you can go chemical and kill all the help I was creating above with a fungicide. It will likely have a higher intitial kill than H2O2/Lactobacillus, but it leaves a vacuum behind it. The first thing to crawl from the wreckage won't be a good guy, and likely be the bad guy you were after. Let's treat the disease (lack of biology to counteract the fungus) and not the symptom (dang fungus).