First off, I played through on medium difficulty.
Letho is tough but like most boss fights he has patterns of attack that you can exploit. These patterns are roughly based on how close you are to him.
If you're in close, his sword attacks are pretty brutal and are difficult to block (but read on for usage of Aard).
If you're in mid range he'll use Igni (fireball) and Aard (to push you back off your feet).
If at long range, he'll use Grapeshots (grenades) and their poisionous variant in combination with his mid range attacks.
He'll always try to close the distance between you.
Regardless of distance though, he uses Quen (the magical shield) a lot. When he has Quen up, keep your distance from him, while dodging his ranged attacks. Don't be tempted to attack him - it takes 2-3 hits to remove it and by then he's probably already hit you. It's easy to avoid the Grapeshots as you familiarise yourself with his body motions as he thows them and they move relatively slowly through the air, Igni and Aard are more difficult to dodge but as long as you keep moving you should be alright.
I beat him using a fairly simple combination of keeping my distance, keep moving, then close in and use Aard on him when his Quen drops to push him off guard then move in for two heavy attacks then run away. As you advance towards him - as you're about to cast Aard (only when his Quen is down) - do so in a diagonal manner - strafe forward and across from his path, don't go head on at him becuase he'll often hit you with Igni or Aard.
You can get two heavy attacks in when you've knocked him off guard, the third, on all my attempts is blocked so I'd say stick to two, rinse and repeat. I didn't bother with the quick attack, I'd say you could probably get three of those in though.
He sometimes goes into weird frenzies attacking thin air, advancing in a stright line, I'm not sure if this is related to how well you're beating him - desparation maybe? Anyway, when he does this, flank him (close in to the left or right of his attack path) get close and use Aard to interrupt his attack and throw him of balance then get two hits in and run away.
I experimented with Yrden to tear his Quen away but in actual fact just avoiding him altogether worked better for me and gave my vigor a chance to replenish.
Once you've had a chance to master the Aard, hit, hit attack pattern, you can finish him off pretty quickly.