While this is a very old question, the current answer has since been outdated as training to build up the "Ace Trainer" medal changed in late 2018.
When the gym system was reworked in mid-2017, the "Ace Trainer" medal was no longer available as you could no longer train in gyms. This was this case until late 2018, when the battle system was implemented. Now, can train by battling against the team leaders in trainer battles.
To begin these battles, tap the "nearby" bar on the bottom right of the screen, and swipe left to choose which leaders you want to battle. Each leader has different Pokemon based on the league you choose. If you win the battle, then your ace medal will increase.
- Great League: Magikarp, Feebas, and Squirtle
- Ultra League: Alolan Ninetales, Glalie, & Lapras
- Master League: Lapras, Gliscor, & Articuno
- Great League: Slugma, Vulpix, and Charmander
- Ultra League: Alolan Marowak, Houndoom, & Infernape
- Master League: Infernape, Electivire, & Moltres
- Great League: Magnemite, Mareep, and Pikachu
- Ultra League: Alolan Raichu, Magneton, & Manectric
- Master League: Manectric, Milotic, & Zapdos