Achievements can act as guide-posts or sign-posts informing your reader of multiple things. Think of them as part of your stat-mechanic structure and ways of warning, informing or congratulating your reader.
1: Warnings - These types of achievements will warn a reader that a consequence of their choices occurred. In your project as an example, achievements dealing with publicity, notoriety and well known vs achievements dealing with aliases, subversion and incognito will warn your readers that they are choosing paths that lead to certain conclusions.
Why is this important when they can look at the stat-page? Well, besides the fact that some readers will never look at the stats, it also serves as a blinking red light on your car’s dash - signalling to the reader that perhaps they should look at their stats now…
2: Informing - These type of achievements act like those highway signs showing what is available at the next off-ramp. The driver sees there is: food, gas, lodgings ahead. The reader is informed by the achievement that they broke through the friendship zone of Ortega, major kissing scene ahead if you chose correctly next choice-body … it prepares your reader for what lays ahead.
Copy-paste the stats thing here: this is important because some people never look at stats, so on and so forth.
3: Rewarding - These types of achievements can encourage completionists and readers to find obscure, difficult or unpopular branches of your story - a pat on the back will keep motivating many people into trying and trying again. In your story, if you have an achievement called: “Crashed Bridal Party” and it is awarded when they go through the plate glass window and literally crash into the display of a bridal party scene in a storefront - if someone did not do that, this would encourage your readers to try to do so. They would be rewarded with new prose, a path not taken by everyone else or some other accomplishment that makes them a special snowflake.
Why? Because everyone loves to be a special snowflake.