These become available when you complete the corresponding task in the indicated mission.

Unlock Mission X-1:
Get a rank of 'AA' or better in mission A-5.

Unlock Mission X-2:
Get a rank of 'AAA' in mission A-6

Unlock Mission X-3:
Get a rank of 'A' or better at mission B-6.

Unlock Mission X-5:
Do less than 5 'GREATs' in mission X-3.

Unlock Mission X-7:
Get 8,500,000 points or more in mission B-30.

Unlock Mission X-9:
Get 8,500,000 points or more in mission X-8.

Unlock Mission X-10:
Do less than 4 'GOODs' in mission B-45.

Unlock Mission X-11:
Do 30,000,000 points or more in mission B-34.

Unlock Mission X-13:
Get a rank of 'C' in mission C-4.

Unlock Mission X-14:
Get 'OK' on ALL Freeze Arrows in mission C-17.

Unlock Mission X-15:
Get 'OK' on ALL Freeze Arrows in mission C-5.

Unlock Mission X-16:
Get a rank of 'AA' or better in Mission C-5.

Unlock Mission X-17:
Get a MAX COMBO of 30 in mission C-16.

Unlock Mission X-19:
Get 'OK' on ALL Freeze Arrows and 180 or more 'PERFECTs' in mission C-22.

Unlock Mission X-21:
Get 8,500,000 points or more in mission C-12.

Unlock Mission X-23:
Get a rank of 'AA' or better in mission D-4.

Unlock Mission X-24:
Get 'NG' on ALL Freeze arrowns in mission D-10.

Unlock Mission X-25:
Do less than 5 'GOODs' in mission D-14.

Unlock Mission X-26:
Get 65 or more 'PERFECTs', 'GREATs' and 'GOODs' in mission D-26 or get less than 6,800,000 in mission D-12.

Unlock Mission X-27:
Get a MAX COMBO of 200 in mission X-24.

Unlock Mission X-28:
Get 200 or more 'MARVELLOUS' in mission X-26.

Unlock Mission X-32:
Get 100 or more 'GREATs' in mission D-18.

Unlock Mission C-21:
Do less than 100 'PERFECTs' in mission C-18.

Unlock Mission C-27:
Get 36,000,000 points or more in mission X-21.

Unlock Mission D-44:
Get a MAX COMBO of 1,000 or more in mission X-30.

Unlock Mission D-45:
Get 50 or 'BOOs' in mission X-31.

Unlock Mission D-47:
Get 35,000,000 or more points in mission D-43.

Unlock Mission E-9:
Get less than 8,600,000 points in mission E-6.

Unlock Survival Mode, Endless Mode and Combo Challenge Mode:
Get ALL the hidden songs in the game and then buy them from the shop. These modes will then be unlocked in the shop.

Unlock Costumes:
Play Dance Master mode with a character for 5 missions and that character's costume will then become available in the shop.