Just shoot em with your railgun because they can fly only straight and they really thicc, also you have chance to oneshot Hyperion with railgun, also Shrike have chance to survive after a lot of Hyperion railgun hits*!
*its true that hyperions have bad rcs thrusters because they basically have design of atmosphere craft and can fly in atmosphere, but anyway they not so easy to hit as pegasus or carrier ship, also chance to oneshot hyperion nearly to zero(but i made it few times) when hyperion railgun much more powerful.....

Equp all slots with missiles and just spam them! Missiles have big warheads and great speed, allows them to kill or heavy damage Hyperion with one hit! Also you can equp 12 missiles, so 4 missiles for one Hyperion gives you 10000% chance to win*!
*hyperions have much better missiles in much more ammount, and they not need to place them instead any other weapon, also ciws can intercept missiles or they can just miss because autopilot sus or they used all dV(or both)

Use asteroids or other things to get in close combat and then dodge their cannons and destroy their weapon with your own, you can aim gimbals to weapons on big vessels so this isnt really hard as you may think*!
*going to close combat with light fighter againt heavy fighters that equpped with armour and 30mm rapid firing cannons not really smart idea, you have +_zero chances to win

Okay you tried all 3 ways many times but every time died? Dont worry, this isnt a game where you will get everything easy, its possible to kill 3 Hyperions in one mission using Shrike, i made it 1 or 2 times, but you need more skill and luck, also you can try other vessels, they could make your gameplay more fun!