Here is the full list of all 38 It's Quiz Time achievements.
A player correctly guesses every clue for a subject in Describe It!
The same player answers every question incorrectly during All in Order
Finish a Solo Score Attack game with zero points
Complete a Solo Score Attack game
Play on December 25th
Play on October 31st
A team of two or more players beats the leader in Showdown
The same player works alone against a team of two or more players in Showdown 5 times
No-one answers incorrectly during a round of Connections
The same player correctly predicts that everyone will answer correctly during Trust or Bust
Complete 10 games with friends
Someone joins mid-game
A player goes from last place after the first round to winning the game
A new player wins the game
The same player is leading at the end of every round and wins the game
The same player wins three games in a row
All players choose the same specialist subject during The Big Finish
A player guesses only one clue during Describe It!
Play two back-to-back games with the same players
All players answer every question correctly during the Starter Round
Complete a game with friends
A player correctly answers all specialist subject questions during The Big Finish
A player scores over 450 points on a single question in The Big Finish
The leader beats a team of two or more players in Showdown
A player answers correctly during Trust or Bust when all other players predicted otherwise
The same player is chosen as the best friend by all players in a round of Best Friends Forever
Everyone answers correctly in Best Friends Forever, apart from the best friend
Best friend fails to correctly predict player's answer in Best Friends Forever
A clue is removed during Describe It! after someone calls 'Shenanigans!'
Someone calls 'Shenanigans!' during Describe It!
Complete 30 games with friends
Complete a game with 8 players
The same player answers every question correctly during All in Order
No-one answers correctly during Trust or Bust
The same player predicts everyone will answer incorrectly during Trust or Bust
All players in a 4-player multiplayer game finish with over 7,500 points
A player scores over 9,999 points in a multiplayer game
Score over 8,000 points in the Solo Score Attack