Shardbearer Radahn is found in Caelid at Redmane Castle. In order to battle him the Festival needs to be triggered which you can do by reaching the Leyndell Captial.
During this fight you will see yellow summon signs that will bring in NPCs to help you in the fight. You can summon a maximum of 6 at a time, and they will fight Radahn for/with you. I would recommend summoning them all at the same time, as 1 on 1 with Radahn they get decimated. If they do die keep riding around on Torrent and the signs will reappear.
Shardbearer Radahn has 2 phases. When you first spawn in he will shoot purple arrows that target you at great speed. Dodge these as soon as he has shot them from his bow, careful they are so fast!
When the NPCs have ran the massive arena towards him he will do strong swipe attacks. I suggest riding on Torrent and swiping at his legs when you have the oppurtunity, but there is no shame in letting the NPCs do the work and just summoning them once they die.
Phase 2 will begin and Radahn will disappear. Don't be fooled, after about 20 seconds he reappears in a massive fire meteorite that will obliterate you, make sure you are moving around at it is easily dodged. He will spawn in 4 purple floating stones around his body, I suggest keeping your distance as these will lock onto you and hit you very hard. More purple smaller floating stones will appear and quickly lock onto you, I would dismount Torrent and dodge manually to avoid these.
I got to a stage where the NPCs summon signs didn't show up after a while, so I had to grit my teeth and slowly whittle him down myself, take your time and wait for his attacks and attack yourself when there is the opputunity.
This is arguably one of the hardest bosses in the game, but so satisfying when you finally achieve your victory!