Here is the full list of all 22 Silver Axe - there are The Honest Elf achievements.
Obtain Anient Cedar Amulet
Defeat Snow White “Insomniac”
Defeat King of Bees
Defeat Grass Whale
Defeat The Master
Defeat Harp
Defeat Cazadora
Defeat Furious Snow White
Successfully encourage Timid Tree
Meet Gran
Obtain Cross of Raid
Succesfully trigger Propolis Bomb
Successfully perform a sneak attack on Grass Whale
Open the Secret Chamber of Ditching Class
Find Boal the Boar's secret camp
Return all elven relics
Break Dr. Squirrel's special scarecrow
Collect all Life Fruits
Defeat King of Bees without using any Aid
Defeat Grass Whale without using any Aid
Defeat The Master without using any Aid
Complete Sliver Axe chapter one