Achievement is one of the motivations found in Quantric Foundry's Gamer Motivation Profile, and has two aspects: Power, and Completion. This analysis uses that model.
Achievement, specifically the completion aspect, is well represented in the goals display of Untitled Goose Game. The player can pull up a notebook at any time during the game to see their goals by location. As they complete the goals, there is a satisfying pencil sound and the goal is crossed out, giving sensory rewards for achieving goals. This also mimics real-world list making exactly, carrying over a familiar sense of satisfaction of checking off all the items on a to-do list. Completing all the goals in the area grants a player access to a new area, but it also allows for this completed to-do list, which is rewarding in itself.
The completed goals don’t disappear entirely, but are crossed out to help maintain focus. This counters the Zeigarnik effect (people remember uncompleted tasks better than completed ones) by continually reminding the player of their accomplishments. This can further their sense of achievement by showing how far they have come. Many games play into the Zeigarnik effect to keep players moving, so this is an interesting twist on an achievement system.