re: What's the key to defeating Lynels in BoTW?

Target them. Hold L1 like a madman.

When it charges you to swipe you with its sword, backflip to avoid. When it charges you without its sword drawn, side-jump to avoid. If you time those just right, you get the slow-mo counter for free hits.

Always keep up your shield out.

When it gets close, it does two attacks: first is a 3-swing attack. Do shield out and backflip each to avoid. Odds are you will activate slow-mo. The second type attack is a double-sword attack. Shield out, backflip to avoid.

When he does either attack, I always backup and backflip. Then I break out my bow and shoot him in the face. He gets stunned and I climb on his back for 5 free hits. Doing this does not degrade your weapon. That hells extend the life of your weapons so you don't wear them all out killing it.

When it breathes fire, I just run sideways then shoot it in the face with a bow, stun it, climb on its back and beat its arse. You can try to parry attacks, but I found it annoying to time it right and actually kinda unnecessary.

The Lynels with the big clubs or spears require slightly different tactics, but the premise is the same as above. There are plenty of vids on YouTube to assist. Good luck.