In order to obtain the Irithyll Straight Sword, you must travel to Undead Settlement area. Travel to the tower from where someone is showering Arrows at you from the start. At the entrance of the Tower, you see someone coming up from the elevator who is actually Siegward of Catarina. Use the elevator to head down to the basement and then head towards the room where you will the Frost Knight. Now he is very quick with his attacks so he can kill you in seconds if you aren't guarded. If you try attacking him with fire he will give up really faster rather than normal heavy combat. Once you take him down he will drop Irithyll Straight Sword, so grab it and start using it.