There are quite a few different visors (visor colors really) that you can unlock in Halo 4, earned in various different ways.
Here is the list I have compiled so far. If you have more to add, please let me know in the comments.
Blindside (Dark Red) – Earn the commendation Avenger – Master
Cyan (Light Blue) – Unlocked with the commendation From the Brink – Master
Frost (White) – Unlocked at rank SR-29
Legendary (Gold) – Complete the campaign on Legendary (Solo or Co-op)
Midnight (Black) – Unlocked at rank SR-46
Recruit (Blue) – Unlocked by default
Solar (Red) – Unlocked at rank SR-20
Sunspot (Purple & Blue) – Unlocked with the commendation Assistant – Master
Verdant (Green) – Unlocked with the commendation Splatter – Master