You must do two things in this boss fight: expose Odolwa's eye weak point, and deal damage to it. There are several ways to do both.
This is the easiest and most common method used. With the Deku Flowers, you can expose the weak point instantly by flying into the air and dropping a Deku Nut on Odolwa. Once you deal damage to the eye, quickly get into a Deku Flower before the boss touches the ground. Sometimes, the boss will stare at Deku Link instead of doing his usual "searching" animation. If you drop the Deku Nut on Odolwa in this state, he will actually fall faster than normal.
This is the harder method. Whenever you throw a bomb or chu at Odolwa, he will always jump into the air and away from the explosive. 5 Arrows will bring Odolwa down and expose his eye. At the beginning of the battle, you want to roll towards the boss 2-3 times, throw a bomb or drop a chu, and once he makes his first jump, land 3 arrows on him. Once he jumps again, shoot 2 more. After damaging the eye, he will jump behind you. Be prepared to aim and shoot those 5 shots again. If he lands and blocks your arrows, you will have to quickly throw another bomb or chu to make him jump.
If you've collected the Zora mask, you can roll behind Odolwa and stun him with Zora Link's shield barrier. After stunning, use two regular attacks, and stun again then use three regular attacks. This will expose the eye.
If you've collect the Goron mask at this point, 5 punches will easily end each cycle. Time the hits as soon as the red flashes of invincibility end.
3 Chus will end each cycle. However, for some reason, each explosive has the capacity to hit the eye twice. Therefore, only 2 explosives are needed at the minimum. Backflip and shield+bombchu to make the explosion happen instantly.
If you've collected the Zora mask at this point, doing a regular attack followed by a jump slash twice will damage the eye for optimal damage. Odolwa will get up and jump, follow his shadow while L-targeting, and use the barrier before he lands to stun him again.