Tier 1 mode is Hard mode without a HUD (Heads-Up Display), and Hardcore mode has no Checkpoints (if you die/fail, you start the Campaign over). Once unlocked, both difficulties are access by starting a new Campaign and changing the difficulty setting.

Unlockable	How to unlock
Hardcore Mode	Complete the Warfighter Campaign on Hard Difficulty.
Tier 1 Mode	Complete the Warfighter Campaign on Hard Difficulty.