The solutions are all listed in chess notation - which you should have learned during the tutorial.

Historic

The Immortal Game

19. e5!
20. Ke2
21. Nxg7+
22. Qf6+
23. Be7#

The Evergreen Game

19. Rad1
20. Rxe7+
21. Qxd7+
22. Bf5+ double check achievement
23. Bd7+
24. Bxe7#

A Night at the Opera

10. Nxb5
11. Bxb5+ Spanish Bishop
12. O-O-O
13. Rxd7
14. Rd1
15. Bxd7+
16. Qb8+
17. Rd8#

The Magnus Effect

24. gxf7
25. Rd3
26. Rg3+
27. Qe5+
28. Qf5+
29. Qd7#

The Gold Coin Game

Note: you're playing as black this game, so look at the right side of the screen

17. Qc5
18. Bxc3
19. Qxc3
20. Nd4
21. Ref8
22. Rh6
23. Rxh3
24. Qg3

The Game of the Century

Note: you're playing as black this game, so look at the right side of the screen

33. h5
34. Kg7
35. Bc5+
36. Ng3+
37. Bb4+
38. Bb3+
39. Ne2+
40. Ne3+
41. Rc2#

Old in chess

15. d5
16. Be3
17. Rd1
18. Rxd5
19. Bf4
20. Qxd7+
21. Qd8#

Blunder #1

32. Rxb7

... and the game becomes non-deterministic. Use something like https://nextchessmove.com/ to win from here.

Blunder #2

69. fxg6+

... and the game becomes non-deterministic. Use something like https://nextchessmove.com/ to win from here.

Blunder #3

Just use something like https://nextchessmove.com/ to win from here.

Mate in 1

Mate in 1 - 01

1. Qf7#

Mate in 1 - 02

1. gxf5#

Mate in 1 - 03

1. Nxc7#

Mate in 1 - 04

1. f7#

Mate in 1 - 05

1. Kxb5#

Mate in 1 - 06

1. Qg7#

Mate in 1 - 07

1. Bc7#

Mate in 1 - 08

1. Nf5#

Mate in 1 - 09

1. Nf7#

Mate in 1 - 10

1. Qg7#

Mate in 2

Mate in 2 - 1

1. QXd6+
2. Re8#

Mate in 2 - 2

1. Nxd7+
2. Nf6#

Mate in 2 - 3

1. Qxb6
2. Nc7#

Mate in 2 - 4

1. Qh3+
2. g3#

Mate in 2 - 5

1. Nxd6+
2. Ne7#

Mate in 2 - 6

1. Qc5+
2. Nf4#

Mate in 2 - 7

1. Qh4+
2. Bd8#

Mate in 2 - 8

1. Qe3+
2. Bc5#

Mate in 2 - 9

1. Qc3+
2. RC5#

Mate in 2 - 10

1. Rb7+
2. Nc6#

Mate in 3

Mate in 3 - 1

1. Qxh6+
2. Rxh6+
3. Bxf6#

Mate in 3 - 2

1. b3+
2. Rb4+
3. Nb6#

Mate in 3 - 3

1. Qxh7+
2. Nxf6+
3. Rh4#

Mate in 3 - 4

1. Qc4+
2. Qc1+
3. Nb3#

Mate in 3 - 5

1. Qh8+
2. Ng6+
3. Qxg7#

Mate in 3 - 6

1. Qc6
2. Rxd5
3. Rd8#

Mate in 3 - 7

1. Qh7+
2. Be5+
3. Bg7#

Mate in 3 - 8

1. Nh3
2. Kf2
3. Ng3#

Mate in 3 - 9

1. Rb7+
2. Rb8+
3. Rd8#

Mate in 3 - 10

1. d8=N Underpromote
2. Qb7+
3. Nc6#

Mate in 4

Mate in 4 - 1

1. Nf6+
2. Qf8+
3. Bh6+
4. Re8#

Mate in 4 - 2

1. Rc8+
2. Qxb6+
3. Nc6+
4. Qd8#

Mate in 4 - 3

1. Ne6+
2. Qe7+
3. Qe8+
4. Ne7#

Mate in 4 - 4

1. Qg7+
2. Qxe7+
3. Rg7+
4. Nf6#

Mate in 4 - 5

1. Qe5+
2. Qc7+
3. Qc8+
4. Qc6#

Mate in 4 - 6

1. Nxf5+
2. Qg5+
3. Nf6+
4. Qh6#

Mate in 4 - 7

1. Ne7+
2. Bd5+
3. Bxe6+
4. Qxg7#

Mate in 4 - 8

1. Rf8+
2. d6+
3. Bxd5+
4. Bxe6#

Mate in 4 - 9

1. Nf5+
2. e6+
3. Qf7+
4. Qxg7#

Mate in 4 - 10

1. Qb8+
2. Qxd8+
3. Bh6+
4. Qh8#

Mate in 5

Mate in 5 - 1

1. Rxh7+
2. Qxf5+
3. Qg6+
4. Qf6+
5. Bxc6#

Mate in 5 - 2

1. Nc6
2. Qc8+
3. Qa8+
4. Qa2+
5. Qe2#

Mate in 5 - 3

1. Qc3
2. Rb6
3. Bxc5
4. Re6
5. Bg6#

Mate in 5 - 4

1. Ba4+
2. b3+
3. Bb5+
4. Rg4+
5. Ne3#

Mate in 5 - 5

1. Qf7
2. Qxg6
3. Re7
4. Kxf3
5. Qxg7#

Mate in 5 - 6

1. g4
2. g5
3. Nb1
4. Nd2
5. Nc4#

Mate in 5 - 7

1. Ne5
2. Nd7+
3. Bh1
4. Kc6
5. Kb6#

Mate in 5 - 8

1. d3+
2. Bd4
3. a6
4. a7
5. a8=Q#

Mate in 5 - 9

1. Ke2
2. Kd2
3. Bh2
4. Ne6+
5. Nac7#

Mate in 5 - 10

1. Qd7
2. Ng5
3. Qh3
4. Qxh6+
5. Rh7

Mate in 6

Mate in 6 - 1

1. Ra7
2. Rxb7
3. Rxf7
4. Bxf7
5. Qf8#

Mate in 6 - 2

1. Qxh7+
2. Rh5+
3. Ng6
4. Kxh2
5. Rh8+
6. Rxf8#

Mate in 6 - 3

1. Rc1+
2. Qb4+
3. Bf3+
4. Qe4+
5. Qxe8+
6. Qxd8#

Mate in 6 - 4

Note: you're black for this one

1. Re7+
2. Re4
3. Kxc7
4. Kd7
5. Kxc7
6. Nf6#

Mate in 6 - 5

1. Bxf6
2. Nxg7
3. Rxh5+
4. f6+
5. Bxe4+
6. Qh6#

Mate in 6 - 6

1. Ne7
2. Nxc6
3. Ne7
4. Nxg6+
5. Rf3+
6. Rxe5#

Mate in 6 - 7

Note: you play as black for this challenge

1. Nf3+
2. Rh5
3. Qc7
4. Rxh7
5. Rxh3+
6. Qh2#

Mate in 6 - 8

1. f6
2. fxe7+
3. Bxf6+
4. Rxh7
5. Qh5+
6. Qh8#

Mate in 6 - 9

1. Qf5+
2. Rxf8+
3. Qxf8+
4. Qf5+
5. Re7+
6. Qc8#

Mate in 6 - 10

1. Qd8+
2. Nxe6+
3. Bg5+
4. Nd8+
5. Rxe3+
6. Rxe6#

Mate in 7

Mate in 7 - 1

1. Qe5+
2. Nc7+
3. Nxe8+
4. Nc7+
5. Na6+
6. Qb8+
7. Nc7#

Mate in 7 - 2

1. Qxg6+
2. Be6+
3. Qxf7+
4. Ne8
5. Qxe8+
6. Bf7
7. Bg6#

Mate in 7 - 3

Note: you play as black on this board

1. Rc1+
2. Qa7+
3. Qxb6+
4. Qxd4+
5. Nf2+
6. Nh1+
7. Qd1#

Mate in 7 - 4

Note: you play as black on this board

1. Qe1+
2. Nf2+
3. Qe4+
4. Qd3+
5. Qf3+
6. Nd3+
7. Qxf2#

Mate in 7 - 5

1. Rc1
2. Qxf1+
3. Rd3
4. Rxf3
5. Qg1#

Mate in 7 - 6

1. Qa3
2. Ra7+
3. d6
4. Rc7
5. Qa7#

Mate in 7 - 7

1. Rxh7+
2. Qh5+
3. Qg4+
4. Bg5
5. Bf6+
6. Rh3+
7. Rxh6#

Mate in 7 - 8

1. Rxh7+
2. Qh1+
3. Qxh3+
4. Qh6+
5. Qh4+
6. Bh6+
7. Bxf8#

Mate in 7 - 9

1. Rxf8+
2. Qh8+
3. Bg6+
4. Qg8+
5. Bf5+
6. Qxe6+
7. Qd7#

Mate in 7 - 10

1. Qh4+
2. Qg3+
3. Bc3
4. Qxc3+
5. Qxd4+
6. Qxf6+
7. Qg7#

By completing all of the tutorials, the rest of these achievements can be earned in one go. The tutorial runs you through all of these moves.

Can be obtained in challenges > Historic > The Evergreen Game

The moves for white are:

19. Rad1
20. Rxe7+
21. Qxd7+
22. Bf5+ double check achievement
23. Bd7+
24. Bxe7#

Start the Historic Challenge Blunder #1

Move the white knight to f4, then hit escape and retry the match

This moves the knight back to e6 and grants the achievement.