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".