By dealing 2 sword slashes to Yuga per cycle, the fight can be completed in a total of 5 cycles. When he is moving around the room as a portrait, if the real Yuga doesn't cross path with any of the other 2 portaits, then you can follow him and know where he will pop out. If he crosses path with another portrait, then the real Yuga can take either one of the two directions, making it impossible to predict where he will jump out.
There is an enemy on the far east of the room in 3F that you are supposed to reach and kill by merging a wall and travelling all the way from across the room. That can be avoided by using the Bow or Ice Rod. For the Bow, shoot it from the highest place in the west portion of the room. Be aware that the enemy moves around, so he might be a pain to take out using this method. For the Ice Rod, simply stand close to him and continuously drop ice blocks until he dies. This method is much faster and is not affected by his movement.
By using the Tornado Rod and an Armos Statue to push yourself while in the air, it is possible to land on any of the pillars in the room. Once on top of a pillar, you can reach the next area by simply walking directly south. The best idea is to do that a bit left of the third pillar (thirs starting from the right wall), so you end up near the next staircase you want to take.
By using the Tornado Rod and the northern Green Soldier on the first staircase, it is possible to get onto the railing and skip going out to the balcony.
First kill the Bomb Solider then lure the Green Soldier to the first set of stairs and stand up against the left railing. Have the Soldier come in on the same plane as you from the right and let him get clipped into Link's body. Use the Tornado Rod once he is clipped and Link should land on the railing below the stairs. Then walk under the northern platform and Tornado Rod and you will clip into it.