Here is the full list of all 41 Math Combat Challenge achievements.
You must win 5 times at the Stadium Arena
You must win 10 times at the Stadium Arena
You must win 20 times at the Stadium Arena
You must win 50 times at the Stadium Arena
You must win 5 times at the Asteroid Arena
You must win 10 times at the Asteroid Arena
You must win 20 times at the Asteroid Arena
You must win 50 times at the Asteroid Arena
You must win 5 times at the Titan Arena
You must win 10 times at the Titan Arena
You must win 20 times at the Titan Arena
You must win 50 times at the Titan Arena
Get 50 books at the stadium
Get 100 books at the stadium
Get 150 books at the stadium
Get 50 books on Titan
Get 100 books on Titan
Get 150 books on Titan
Destroy 20 fighters
Destroy 50 fighters
Destroy 100 fighters
Destroy 20 starships
Destroy 50 starships
Destroy 100 starships
Promoted to Math Cadet
Promoted to Math Soldier
Promoted to Math Sergeant
Promoted to Math Lieutenant
Promoted to Math Commander
Promoted to Math Captain
Promoted to Math Rear Admiral
Promoted to Math Vice Admiral
Promoted to Math Admiral
5 missions with 0 errors in dynamic panels
10 missions with 0 errors in dynamic panels
5 missions with 1 error in dynamic panels
10 missions with 1 error in dynamic panels
5 missions with 2 errors in dynamic panels
10 missions with 2 errors in dynamic panels
5 missions with 3 errors in dynamic panels
10 missions with 3 errors in dynamic panels