Here is the full list of all 15 I Know Everything achievements.
Get to the top 10 for all players in single-player games
Win a 30-question game against the computer
Win a 60-question game against the computer
Win in the "Russian literature" category
Win in the "World literature" category
Win in the "Mathematics" category
Win in the "Cuisine" category
Win in the "Astronomy" category
Play with no opponent and win a 30-question game
Win a game without making a mistake
Visit the main menu
Win a 15-question game against another player
Win a 60-question game against another player
Play with no opponent and win a 60-question game
Get to the top 10 for all players in multi-player games