Engage with missiles while he does his Kulbit and Kvochur's Bell maneuvers. SASMs also help .

Ive ran out of missiles twice and failed because of time. I cannot hit him with guns and i really dont want to restart the whole mission just to beat him. This really killed my entire drive for this game

Sadly, Guns is the best tactic. For future replays, the X-40 with Lasers UAV's works wonders

Your best bet is spamming high-G turns and PSM to get missiles on target, I beat him on ace using that method

SASM spam is one easy way. otherwhise yeah get those guns skills up. atleast thats what i did and do when i can since i do the different role runs and attacker and ew wasnt super fun for that mission

SASMs make the fight against Shadow 22 and his cohort super easy.

I had a far superior time killing these guys with low tier MiG-21 + SASM missiles than I did F-22 + QAAMs.

I just made it a point to land and rearm in anticipation for this fight.

All you need to do is keep an eye on your radar and make sure to only shoot missiles when you're actually behind them. Don't fire just because it locks on, if you see that the enemy chevron is not pointing "North" on your radar you won't hit. But if you are behind them the missile will reliably hit.

Gotta gun him down when hes flaring or doing his trickshot, shooting him down first makes the fight easier.

If you haven't done it already, changing to the type-b gunsight is way easier to use in my opinion. Makes using the MG/MGP much easier.

Use standard missiles to get them to pull the kulbit, then hit them with SASMs, QAAMS, or guns.

Also, saturation of fire is very valid. Have your wingmen focus on one Shadow at a time.

I have met one Ace pilot who have had said that there were pilots like you in every generation. and he had also said that he had felled every last one of them. I remember he also wanted to understand the enemy.... just a tip, do post stall maneuver like kulbit or cobra on them and then machine gun

Always try to release missiles when the hud says "SHOOT" during a lock-on, this will toggle special properties for the missile. I believe it is called Magic Missile, but i am not 100% sure. The hit rate goes up substantially.

I just kept shooting at him until he decided to do reverse fly straight at me and eat a QAAM to the face and died.

Guns or SASMs sprinkled in with regular missiles. If you go that way, open up with a missile, wait half a second so he finishes the dodge on the missile and dump a SASM, he'll eat the SASM 90% of the time (unless you shoot at a time where it's clear that's not gonna happen, such as during one of his PSM, or at a bad angle)
Repeat until dead.
If that doesn't work for you, it's guns time baby.

SASMs worked very well for me, I defeated all the shadows it 5 mins with the FA36, make sure to use the upgrades that cause them to do more damage and have a wider blast radius as well as other air to air upgrades and capacity