How can I beat Lynels?

One easy way is to use the lightning strike from the Gerudo Divine Beast - it deals about 500 damage per hit. Given that it'll also stun the Lynel, you can probably kill it very easily between uses.

Melee attacks are your best bet, since at range they have some pretty nasty arrows.

I defeated a Lynel like this:

First, you should have at least 8 hearts and proper defensive gear/armor, since his strikes deal heavy damage. In case you get hit, eat something immediately. Go for extra hearts, defense or damage with your meals. Fairies don't hurt either.

Never try to defeat him from distance! His aim is ludicrous and his shock arrows deal tons of damage.

Flurry is your friend. I dealt the most damage waiting for his melee attack (the one where he stands, not the one where he gallops) and backflipping in the right moment (Y + Analog Stick Down). Then you'll get the chance to do a flurry attack with Y, hitting him many times. Use a hard hitting weapon.

You have to be patient. Without spoilering, the special reward from defeating the elephant divine beast is a big help.

Good luck!

You can stop a charge by using upgraded Stasis on them. It'll hold them for around 1-2 seconds, which should be just enough to fire an arrow into their face. When they come out of stasis, they'll be staggered and their charge will end.

My favourite strategy is to try and stun lock them. First, you need to hit it in the face with a powerful enough bow. Doing so will force it down on it's knee for a short while. While in this state, you can approach them and press 'A' to mount them. This allows you to get about 5 hits in depending on your stamina and how fast you can mash Y.

I found that if you use an ancient arrow you can kill him in one hit. You can get one from Beetle on "customer appreciation day" whatever that is. The sad thing is, you don't get any reward. ;-;

The strategy I have discovered allows me to run through several of the most powerful Silver Lynels in a row, without the need of a bunch of weapons.

Preparation

1. Complete Ancient Armour set, upgraded at least twice each. The set bonus, Ancient Proficiency, doubles the damage of Ancient weapons. If the armour is upgraded four times, it also has the highest defence in the game.

2. A high damage Ancient weapon, of any type. I had a 60 damage Ancient Battle Axe++.

3. A fair number of arrows, of any type. A good damage bow doesn't hurt, and you'll get a new one off the Lynel.

4. Some food or an elixir which increases attack or defence isn't a bad idea. Environmental protection is another option, if you'd rather not take constant damage if in a cold or hot area.

Combat

1. Run away from attacks, and keep a medium distance. Far enough that he tries to charge at you, but also not so far that he pulls out his bow. Make sure you get away from his ground stab which makes a sphere of fire around him.

2. Shoot arrows at his face whenever you get the chance. This will stun him. The type of arrow doesn't matter, and while bomb arrows will deal more damage at this stage, they do not make it any easier to stun.

3. Whenever he's stunned, run up and mount him, then attack. Weapons do not lose durability while mounted on a Lynel. Your double damage Ancient weapon will take out a hunk of his health.

4. Run away. It's helpful to move the camera facing forward before being kicked off the mount, to more easily keep him in view afterwards. Rinse and repeat.

A little bit of advice from a newbie (5 hearts, 12-15 armor, great fire sword as primary weapon, 40 shield, knight bow): The Lynels that I have found have typically been around cliffs. In attempt to avoid being seen, I climbed up them, and proceeded to shoot him with an ice arrow. After freezing him, I glided over until I was directly above him, hit B to drop, and Y for a flying attack with the great flame sword. This does MASSIVE damage. Fire and ice combo after being frozen is sweet. You may or may not be able to get a few more hits in after that depending on how lucky you are... Run away and repeat. Make sure he doesn't see you because his shot is impeccable! Repeat until you are out of ice arrows. Then, move to regular arrows and use the stun/mount trick previously mentioned. High, protective ground and a ton of arrows! Worse case scenario you throw bombs at him for forever. You can also try throwing a boomerang at him, as it is the right range to not be hit by the bow, but being able to avoid the charge and fire blast. I haven't really experienced this however... Good luck!

Listen: I killed a Silver Lynel (coliseum ruins) in 20 mins with max hearts and the master sword. This is extremely advanced in the game. I recommend killing the Lynel by skill, starting with the red ones and moving up.

My first Lynel was the Zora one (just to say, I bought all of the shock arrows in Gerudo Town and just killed him for fun) I had 3 hearts and a knight’s claymore. What works is stunning him, then charging a two-handed weapon attack. It works like a charm :) Mounting doesn’t always work, and if you have low stamina it doesn’t give you enough of a time window to attack well. (As a side note, I wish you could actually ride a Lynel like a deer or something, with him attacking you the second you dismounted.)

No matter where you are in the game, I recommend avoiding the Lynel.