How do I damage Thunderblight Ganon?
According to the Zelda Wiki entry on Thunderblight Ganon, as well as my own experience fighting him:
Phase 1: The strategy here is straightforward, though it may take some practice: block his attacks, and after blocking his attacks, you should have time to attack once or twice. I used a spear because of the reach (I found it helped land an extra hit), though I am sure many other weapons (eg Master Sword) could be used as well. However I would recommend staying away from 2-handed weapons, as they lack the speed to land the necessary hits.
Phase 2: I found this phase the easiest. After getting his health down to 1/2, Thunderblight Ganon will begin levitating out of reach, dropping pillars around the room which he strikes with electricity. Use Magnesis to pick up a pillar and shock Thunderblight Ganon with a pillar he has charged with electricity.
Phase 3: Now Thunderblight Ganon will repeat his method of attack in the first phase, but much faster and more aggressively. This is the phase I always had problems with, but the strategy remains the same: block when he attacks, and make good use of the limited time after the block to land a hit or two.
If you're still having trouble, you can also use some food or elixirs that give you high electricity resistance to minimize damage during the fight (eg Electro Meat Skewers or Electro Elixir). A good list can be found here, just search for "Electro".
As per Jeff's comment I believe I just regular dodged and hammered attack when he comes in to hit you, I had the Master Sword but any sword or spear (for their quick attack compared to two handed weapons) should do I would say. If I remember rightly he is fast but if you can dodge his attack he should stand still long enough to be hit a few times, and I believe if you attack his shield it gets damaged and destroyed so he can't block.
Later on (after half health) is when he gets really tricky... But I won't spoil that for you if you haven't reached that part yet (unless you want tips for that part of the battle too) and I can't see how to do spoiler tags from my phone.