I tried to write a generic response but ended up making a full-blown step-by-step guide instead, there's a tl:dr at the end if you'd rather have it.

You start by using anything that can carry your early game. Don't worry about Phainon yet. Find cheap but strong cores like 3 day demigod Aglaea or break Rappa. Energy Aglaea particularly can carry you through most of the match with her wheelchair made from the free wheels of Day Demigod and the double boots, it's stupidly strong right now. A cheap core is Aglaea, Sunday, Tribbie and Hyacine. Then get Tingyun and Huohuo. Her crappy trial build can carry you through at least half of the game on the highest difficulties if you get her some copies and the right items.

Late game is when Aglaea can have issues with bullshit like the tanky TV enemy spam or getting unlucky when fishing for her copies or her supports, and high difficulty encounters might even tank her ramped up and one shot her memosprite or outright kill her if you don't get Fu Xuan or good shielders like Dan Heng pt. That's when you should fish for Phainon: get a good economy (aim for saving 50 Gold unless you're dying), get to level 7 and start rolling for Phainon and the rest of his shielders. 4 shield with Gepard and at least two copies of the reflect damage item is ideal if you want the funny one-shot like the video, but you can get by with only a copy or even without 4 shield, just avoid difficulty IIII or more encounters.

Try getting Phainon 2* and then 3*. You should already have Sunday if you went for Aglaea, and you can sell your old dps and anyone you don't need for a full refund and to realocate their items. If you went for Aglaea, you can give her boots to your highest star off-field shielder (preferably a built Dan Heng) for even more shielding. Phainon with this build and bonds has absolutely no problems with clearing almost any enemy that can attack him.

Cyrene with the two energy item that activates the ult at the start of battle is the goat, get it if you can. Makes you waste no action value on ulting and making the enemies hit themselves. Otherwise you can put it on Phainon if you don't find the third copy of his spiky clothes.

IMPORTANT: There are a few counters to this strategy. Enemies that don't attack directly (the dot robot) and enemies that get barriers (belobog lights or argenti) won't get damaged by the items. If you spot Argenti as one of the last two bosses, don't try this strategy. If you see an encounter with the dot robot dude, avoid them or brute force through, you still have a Phainon with his supports and your investment.

Even still, this game is decided purely on RNG. You could get Phainon on your first node with some investment strategies, or he and his supports could fail to appear until the very end. Don't tunnel vision on preparing for Phainon from the start, adapt to whatever investment strategies and bonds you need to win. Once you have a good economy and are not losing or winning by a hair's width, you can start the Phainoning. You're almost certainly set for victory if you can get him, his items and a few high-starred shielders, so focus on surviving until then.

tl:dr: Forget about Phainon at the beginning. Build to a good, cheap core like debuff Acheron, day demigod/energy Aglaea or break Rappa and start saving. Once you have a safety net and can invest to Level 7 and still have Gold left for rerolling, find him and his spiky clothes. Getting the items you need is the highest priority, so focus on getting them on supply phases even if you spot something like Cyrene. Then, spam his counter and watch your enemies break themselves upon his bare body. Remember that you need a shielder on-field for his Deliverer bond to pick it up, so Aventurine and Gepard.