You have to climb the walls to reach the trainers and the gym leader. There are two trainers that you can avoid but I'll suggest against it since you won't be able to fight them again after defeating the gym leader. Besides, the experience and cash prize will go to waste if you bypass them.
The first trainer is located in the eastern side of the tower.
Rising Star Didier (Prize Money: P1,380)
After defeating Didier, climb the wall directly behind him then climb down on the next ledge. Follow the path and climb the next wall if you want to challenge one of the gym trainers there.
Hiker Craig (Prize Money: P1,344)
Get back on the main ledge and follow it to the back where another trainer is waiting for you.
Rising Star Manon (Prize Money: P1,320)
Climb to the next ledge and continue to meet up with the next gym trainer.
Hiker Bernard (Prize Money: P1,176)
Continue to the top and you'll finally face the gym leader.
Gym Leader Grant (Prize Money: P4,000)
Rewards:
After defeating Cliff, climb down using the narrow wall on the left side then slide down to the ground floor.
Heal up your pokemon and before moving on to the next route, it will help you clearing the second part of the Connecting Cave. You can find the entrance on the topmost road. Teach Strength to a pokemon you're planning to use temporarily so you can navigate the cave.