To reach Exeggutor Island, you'll need to head to the south-west corner of Seafolk Village and chat to the chief who's standing next to the S.S. Magikarp. After being ferried to the island, head north through the grassy area, and back to the top of the hill where you obtained the Sun or Moon Flute. You'll find Hapu in front of the pedestal.
Island Kahuna Hapu
As you'd expect from a Mudsdale rider, Hapu is a Ground-type user. Her first Pokémon, Golurk is an evolved Golett with high Attack and decent bulk. It can use Earthquake and Shadow Punch for STAB, Hammer Arm to hurt Ice and Dark-types, and Stealth Rock to annoy switch-ins. Confront it with Grass or Water-types.
Next up can be Gastrodon, which is an evolved Shellos with high HP and decent special-based stats. Hapu's Gastrodon can use Muddy Water and Mud Bomb to deal STAB damage and potentially lower Accuracy, and Recover to restore HP. Grass-types are ideal, as their attacks do 4x damage. All other Types hit neutrally.
Flygon is a fully evolved Trapinch and Vibrava, with high Attack and Speed. This one focuses on offense, relying on Earth Power and Dragon Breath to inflict STAB damage. Ice-types are strongly recommended, as they do 4x damage with their attacks. Otherwise Fairy-types should do well, especially if they have special bulk.
Finally, Hapu has a Mudsdale as expected. This evolved Mudbray boasts stellar Attack and impressive bulk, but suffers from poor speed. It can use Earthquake for STAB damage, Heavy Slam and Double Kick to hurt Ice-types, and Payback for all other purposes. Of course, it has Groundium Z. Tackle it with Grass or Water-types.
Stand your ground against Hapu's might and you'll be awarded with her Groundium Z . With this, you've completed your final Grand Trial! Now all Pokémon that are Level 80 will obey your command, even if they came from a trade. At this point, there's only one more thing standing between you and the title of Island Challenge Champion--the Pokémon League itself!
Dining with Hapu
After defeating Hapu, she'll show up at the restaurant in Seafolk Village if you try and order the "Zumongous Z-Noodles". Like the Olivia and Nanu events, this will allow you to receive 2 Heart Scales free of charge once per day. However, unless you're a huge Hapu fan or really need Heart Scales, eating with Nanu and/or Olivia is a lot more efficient use of time.
An Egg-citing Discovery Or Two
If you're ever bored, fly back to Exeggutor Island and return to the area with the pedestal where you got the flute and battled Hapu. As you climb up the final slope, it will start to rain heavily and the village chief will come over to direct you to the nearby shelter. Afterwards, if you return to Exeggutor Island during the night, you'll learn a secret about the Exeggutor here.