Here is the full list of all 99 Q achievements worth 1,000 gamerscore. It takes around 80-100 hours to unlock all of the achievements on Xbox One.
Drew the same amount as the Giza Pyramid's in height
During the draw test, meet the moai
Cleared PRIMARY 3 Q.46 with only 1 move
Cleared PRIMARY 3 Q.45 with only 1 move
Cleared PRIMARY 2 Q.36 with only 1 move
Cleared SECRET 1 Q.2 with only 1 move
Cleared SECRET 1 Q.1 within 10 moves
Cleared SECRET 1 Q.7 with only 1 move
Cleared PRIMARY 2 Q.35 with only 1 move
Cleared PRIMARY 2 Q.26 with only 1 move
During the draw test, meet the sumo wrestler
During the draw test, meet Alex
Cleared PRIMARY 2 Q.33 with only 1 move
Cleared PRIMARY 2 Q.31 with only 1 move
Drew the same amount as 777,777 hamburgers' in weight
Cleared everything but PRIMARY 1 Q.8 with only 1 move
Completed all of PRIMARY 1
Retried 1500 times
Retried 700 times
Drew the same amount as the Sky Tree's 1/10 height Tree's height
Placed 5 balls in the plate
Drew the same amount as 300 sumo wresteler's weight
Cleared PRIMARY 2 Q.24 with only 1 move
Drew the same amount as Stonehenge's circumfrence
Retried 300 times
Cleared 10 Q's with only 1 move
Drew the same amount as Sagrada Familia's 1/10 height
Switched view and saw least amount of moves and number of players cleared
Drew 1 elephant worth in weight
Retried 100 times
Drew 10 tonnes worth of line
Retried 50 times
Drew 2 tatami worth in area
Drew 20,000 sushi worth in weight
Cleared up to PRIMARY 1 Q.4
Drew for the first time
Complete all of PRIMARY 2
Complete all of PRIMARY 3
Complete all of SPECIAL 1
Complete all of SPECIAL 2
Complete all of SECRET 1
Clear SECRET 2 Q.38
Complete all of SECRET 2
Secret Achievement
Draw the same amount as the height of Mt. Fuji
Clear SECRET 1 Q.18 10 times
Clear PRIMARY 2 Q.34 with only 1 move
Clear PRIMARY 2 Q.38 with only 1 move
Clear PRIMARY 3 Q.43 with only 1 move
Clear PRIMARY 3 Q.54 with only 1 move
Clear PRIMARY 3 Q.56 with only 1 move
Clear PRIMARY 3 Q.58 with only 1 move
Clear SECRET 1 Q.11 with only 1 move
Clear SECRET 1 Q.13 with only 1 move
Clear SECRET 1 Q.15 with only 1 move
Clear SECRET 1 Q.19 with only 1 move
Clear SECRET 1 Q.20 with only 1 move
Clear SPECIAL 1 Q.1 with only 1 move
Clear SPECIAL 1 Q.11 with only 1 move
Clear SPECIAL 1 Q.14 with only 1 move
Clear SPECIAL 1 Q.20 with only 1 move
Clear SECRET 2 Q.21 with only 1 move
Clear SECRET 2 Q.22 with only 1 move
Clear SECRET 2 Q.23 with only 1 move
Clear SECRET 2 Q.24 with only 1 move
Clear SECRET 2 Q.25 with only 1 move
Clear SECRET 2 Q.27 with only 1 move
Clear SECRET 2 Q.31 with only 1 move
Clear SECRET 2 Q.32 with only 1 move
Clear SECRET 2 Q.36 with only 1 move
Clear SECRET 2 Q.37 with only 1 move
Clear SPECIAL 2 Q.23 with only 1 move
Clear SPECIAL 2 Q.24 with only 1 move
Clear SPECIAL 2 Q.28 with only 1 move
Clear SPECIAL 2 Q.30 with only 1 move
Clear SPECIAL 2 Q.31 with only 1 move
Clear SPECIAL 2 Q.32 with only 1 move
Clear SPECIAL 2 Q.33 with only 1 move
Clear SPECIAL 2 Q.36 with only 1 move
Clear 30 Q's with only 1 move
Clear 55 Q's with only 1 move
Play for 10 hours