How can I catch better fish in Hades?

hades

I've got a minor prophecy that I need to catch a "very rare" fish in order to complete. I've fished up dozens and dozens of fish by now, but have yet to see a very rare fish. Are there any keepsakes, boons, or strategies that can up my odds of catching a very rare fish?

There's a fishing-related boon but it only increases the number of fishing points for the run, not the chance to get a rare one.

There are two parts of catching a good fish: timing and luck. There are two possible types of catch, and only the second one has a chance to give you a rare fish.

When you're kinda slow and you get a "Catch!", you can only get one of the first two tiers of fish for this biome: "common" and "uncommon" (I don't think there's an official name for the rarity, e.g. for Tartarus common is Hellfish and uncommon is Knucklehead)
When you're fast enough to get a "Perfect Catch!", you'll get either an "uncommon" or a "very rare" fish, which for Tartarus is the Scyllascion. I'm not sure of the exact percentages, but it's close to 50/50 - the name "very rare" is kind of misleading, I've had runs with 3 fishes that were all "very rare".

Maybe you've been getting perfect catches and were just out of luck, but in case you're only getting basic ones (as was my case for a while) and to help anyone who might read this later (mostlty relevant for keyboard users, from what I know it's much easier with a controller due to the vibration), here are two tips that have helped me getting many rare fishes:

There can only be a maximum of 3 "fake bites", so when the bait goes down for a fourth time it will always be a good catch. Knowing that should help you be faster and get a perfect catch at least 25% of the time (assuming the "real bite" is distributed randomly)
A bit more tricky to use, but I've noticed that the more you wait for a bite, the more likely it is to be fake. So when it bites early you should click the button, but after a few seconds (I haven't properly timed it, you learn it by experience) you should relax and then start again with the next one.

The Hades wiki has more in depth stats about fishing https://hades.gamepedia.com/Fishing and to add to what is already here the rate for a legendary fish (i.e. the rarest and one you're after) is 5% with a perfect catch with the threshold for perfect being <0.34 seconds and the rate for rare fish is 5% with a normal catch and the threshold for normal being slower than perfect but faster than 1 second. In terms of strategies if the stakes are low enough, buying fishing points from the Well of Charon gives more chances to roll the lucky 1/20, starting Hypnos trinket and the deep pockets mirror bonus if unlocked starts you with a decent chunk of obols to spend on early wells. Besides that given the 80% chance to see a fishing point in