You have to cross the water. There are two things to do before that. YOu have to beat your rival at the MegaMart in Lilycove and to beat the Team Aqua from their base at the shore of Lilycove.
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Head to lilycove city then surf east to mossdeep city go into the gym and defeat the leaders for badge #7. Finally one more to go, go into steven's house which is in mossdeep city talk to him to get the HM Dive use it to reach sootopolis city this is where the last gym is!
No, Aerial Ace is not a purchasable TM in Pokemon Emerald. You can obtain it by defeating Winona.
You get aerial ace when you defeat Winona the gym leader in Fortree city.
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fortree city vs winona