Pass her to the south and then carefully shove the floating rock away to the right rather than towards the obvious boulder South of you.  This opens up a passage around said obvious boulder, letting you grab the Escape Rope sitting on the ground.  Head East from here between the raised ground, then turn to the South and descend the stairwell that you find right away to encounter a hiker.

Battle: Hiker Jeremy (1024 Poke)
Opponent: Onix Lv 32, Boldore Lv 32

South from the Hiker you can locate a Metal Coat under the eye of an Ace Trainer, who is thankfully up on a ledge instead of down here with it.  The Metal Coat is a dual-purpose item- it can be held to improve the power of Steel attacks by 20%, or it can be held by an Onix or Scyther that is being traded to allow the pokemon to evolve once the trade is complete.

Step around to the East and then North and you can pick up an Electric Gem at the end of the path, then return to the stairs beside the Hiker and ascend.

Attract the attention of the Ace Traner and she’ll challenge you to a three-on-three Rotation Battle.

Battle: Ace Trainer Vicki (1980 Poke)
Opponent: Ferroseed Lv 33, Stoutland Lv 33, Krokorok Lv 33

Vicki’s a tough fight mostly because of her Ferroseed and Stoutland- the Krokorok’s main contribution is Embargo, which can not only stop you from using healing items but also prevents an affected pokemon from getting a benefit out of its hold item.  Ferroseed puts Iron Defense together with its already high durability and Iron Barbs ability to chip away at physical attackers while sustaining their assaults, and Stoutland is its usual highly durable Work Up- abusing self with a Take Down attack.