Some of the challenges can not be completed, such as the Chapter 2 Season 2 Tourist Trap, which requires a Damage Trap but they are currently vaulted. Some of them are only available during limited-time game modes such as a challenge where a player must eliminate an opponent with a Pumpkin Launcher from 50m away. This is due to the fact that some are very rare, such as the achievement to catch a Mythic Goldfish.
There are multiple challenges, and it is most likely impossible to unlock them all. They are obtained by doing certain challenges. Legacy Achievements were added as a new implementation in Chapter 2: Season 1.
An example of the view of achievements you have earned.