As soon as you enter the boss room you can perform a jumpslash into the intro cutscene (making sure not to store Deku Stick damage as Odolwa is immune to Deku Sticks) to store damage for Power Crouch Stabbing on the Japanese version.
It is easiest to stun Odolwa with an arrow, but it can be fast to stun Odolwa with a jumpslash, especially if bow isn't equipped already. From the beginning of the fight, this can be done by standing on the green stripe and listening to the two syllables Odolwa speaks: Jumpslash after hearing the first syllable for the third time. This is demonstrated in the videos below. There is a chance Odolwa will delay its first attack; in this case, jumpslash again after hearing the second syllable for the fourth time.
Using Power Crouch Stabbing you are able to stun-lock Odolwa, preventing the fight from proceeding to the 2nd phase.
Due to Power Crouch Stabbing being patched in the English version, a slightly different strat is used. Leave space after the third quickspin so that Odolwa doesn't jump away during the fourth.
Using the increased damage of the Great Fairy Sword, you are able to kill Odolwa with a single jumpslash and quickspin.
Stand behind Odolwa to avoid letting Link fall off the flower.