I know you said you know the trainer/grand trial/league stamps, but I may as well add them anyway.
Official Pokemon Trainer
Get your trainer passport.
Melemele Trial Completion
Clear the grand trial on Melemele island.
Akala Trial Completion
Clear the grand trial on Akala island.
Ula'ula Trial Completion
Clear the grand trial on Ula'ula island.
Poni Trial Completion
Clear the grand trial on Poni island.
Island Challenge Completion
Become the first champion of Alola.
Melemele Pokedex Completion
Catch all of the Pokemon found on the island and show your Pokedex to the game director at Gamefreak in Heahea City.
Akala Pokedex Completion
Catch all of the Pokemon found on the island and show your Pokedex to the game director at Gamefreak in Heahea City.
Ula'ula Pokedex Completion
Catch all of the Pokemon found on the island and show your Pokedex to the game director at Gamefreak in Heahea City.
Poni Pokedex Completion
Catch all of the Pokemon found on the island and show your Pokedex to the game director at Gamefreak in Heahea City.
Alola Pokedex Completion
Catch all of the Pokemon in Alola and then show your Pokedex to the game director at Gamefreak in Heahea City. Apparently you get a different stamp depending on what version you play.
50 Consecutive Single Battle wins
Achieve 50 consecutive wins in Single Battles at the Battle Tree.
50 Consecutive Double Battle wins
Achieve 50 consecutive wins in Double Battles at the Battle Tree.
50 Consecutive Multi Battle wins
Achieve 50 consecutive wins in Multi Battles at the Battle Tree.
Poke Finder Pro
Get the final version of the Poke Finder.
Source, and also some searching on other places
Hope I helped!!
