EPT
Plus I had to do a lot of guess-work due to not knowing exactly how the fusion rules work and not having all the information on your personas. I'm going to hope for the best, but this persona would be quite good if this recipe ends up being successful 
There's about 5 fuses in total. Each fusion has some specific rules you need to follow, so be very prebeared to spend a long time on this. Also, save between each step.
+ Show Spoiler +
The goal of this recipe is to fuse Pyro Jack and inherit the following 3 skills:
- Auto-tarukaja
- Fire Boost
- Invigorate 2
By itself, Pyro Jack will learn maragion, auto-rakukaja and resist ice, but it may require a bit of leveling after the fuse to learn everything.
1) Get to level 32 on your main character
1a) Optional goal: Get Yosuke's social link as high as possible.
2) Get a level 15 Eligor. There's two ways you can go about this:
i) Fuse Orobas + Cu Sith
Eligor can inherit absolutely anything here from the fusion.
ii) Buy a base Eligor (level 12) and level it up 3 times
Depending on your social link rank with Chie, you might need to do 2 anyway. Doing the first step can speed it up a little. Just a reminder that you can do the same thing you did with Ukobach in the Jack Frost fusion for fast leveling (except in Rise's dungeon this time).
At level 15, Eligor learns Fire Boost.
3) Fuse Eligor (from above) + Valkyrie
The result is Jack Frost, but you already have one. This Jack Frost is a temporary stepping stone for this recipe, don't worry if it sucks ass (which it will). If you're currently carrying another Jack Frost, you need to discard that one first. When you fuse this Jack Frost, do NOT save it to your compendium.
Jack Frost must inherit Bufu and Fire Boost, but NOT any physical skills (Poison Skewer and Cleave). Should be pretty easy.
4) Fuse Jack Frost (from above) + Mokoi
The result should be King Frost. Once again, King Frost must inherit Bufu and Fire Boost, but NOT any physical skills (Sonic Punch and Hysterical Slap).
5) You now have 3 ingredients to make Pyro Jack with the 3 skills we want:
King Frost (Fire Boost) + Rakshasa (Auto-tarukaja) + Ganga (Invigorate 2)
But Rakshasa is not a very good persona to make Pyro Jack because it has a tonne of physical skills, which Pyro Jack will favour over the 3 skills we want. Thankfully, Titan of the same arcana as Rakshasa, can give us the same result. Proceed to step 6 if you want an easier time making Pyro Jack.
6) Fuse Rakshasa + Valkyrie
The result should be Titan. Titan must inherit auto-tarukaja. Bonus points if it inherits bufu as well. Titan must try not to inherit any physical skills (most of the skills from Rakshasa, unfortunately). This one might be a little difficult. If it ends up taking too much time, 1 physical skill inherited is acceptable.
7) Fuse King Frost (from above) + Titan (from above) + Ganga
Pyro Jack must inherit Invigorate 2, Fire Boost, and Auto-tarukaja. It's easier than the method from step 5, but still very very difficult. Keep redoing until you get all 3, it'll be worth it
If you successfully made this Pyro Jack, then Phoenix is already obsolete
You leveled much faster than I expected, and I didn't account for the low rank Sun link when making the Phoenix, so it actually didn't get very strong in the end. Sorry!
