The achievements in Icecrown Citadel are divided into four main categories: Challenge Achievements (for the meta-achievement), Kill Credits (for progression and titles), the Meta-Achievements themselves (for the mounts), and the Feats of Strength.
Challenge Achievements (The "Glory" Requirements)
These achievements test your raid's coordination with a specific, difficult mechanic on each boss. They are available in both 10-player and 25-player modes unless specified.
Lord Marrowgar: Boned (Defeat the boss without anyone staying impaled by a Bone Spike for more than 8 seconds).
Lady Deathwhisper: Full House (Defeat her with at least five different types of cultists alive).
Gunship Battle: I'm on a Boat (Win the fight without any raid member visiting the enemy ship more than twice).
Deathbringer Saurfang: I've Gone and Made a Mess (Defeat him before Mark of the Fallen Champion is cast three times).
Festergut: Flu Shot Shortage (Defeat him while no player ever reaches 3 stacks of Inoculated).
Rotface: Dances with Oozes (Defeat him without a Big Ooze casting Unstable Ooze Explosion).
Professor Putricide: Nausea, Heartburn, Indigestion... (Defeat him without the Abomination pilot using the Regurgitated Ooze ability).
Blood Prince Council: The Orb Whisperer (Defeat them without anyone taking more than 23,000 spell damage in a single hit).
Blood-Queen Lana'thel: Once Bitten, Twice Shy (25-Player Only). This is a personal achievement requiring two kills: once as a vampire, and once without becoming a vampire.
Valithria Dreamwalker: Portal Jockey (Enter every single Nightmare Portal before healing her to full).
Sindragosa: All You Can Eat (Defeat her without any raid member exceeding 5 stacks of Mystic Buffet).
The Lich King: Been Waiting a Long Time for This (Allow Necrotic Plague to reach 30 stacks before defeating him in Phase 1).
The Lich King: Neck-Deep in Vile (Kill every Vile Spirit before it explodes. Note: This is required for the 25-player meta but NOT the 10-player meta.)
Kill Credit Achievements (Progression & Titles)
These track your progression through the instance on Normal and Heroic difficulties.
Normal Mode (10 & 25 Player)
Storming the Citadel
The Plagueworks
The Crimson Hall
The Frostwing Halls
The Frozen Throne (Defeat the Lich King)
Title Reward for defeating the Lich King on Normal: The Kingslayer.
Heroic Mode (10 & 25 Player)
These mirror the Normal mode achievements but are appended with "Heroic."
Heroic: Storming the Citadel
Heroic: The Plagueworks
Heroic: The Crimson Hall
Heroic: The Frostwing Halls
Bane of the Fallen King (10-Player Heroic Lich King)
The Light of Dawn (25-Player Heroic Lich King)
Title Reward for 10-Player Heroic Lich King: Bane of the Fallen King. Title Reward for 25-Player Heroic Lich King: The Light of Dawn.
Meta Achievements (Mounts)
These are the two top-tier achievements that require finishing nearly all the challenges and heroic kill credits.
Glory of the Icecrown Raider (10 Player): Rewards the Reins of the Bloodbathed Frostbrood Vanquisher mount.
Glory of the Icecrown Raider (25 Player): Rewards the Reins of the Icebound Frostbrood Vanquisher mount.
Feats of Strength (Prestige)
These are ultra-rare accomplishments that award no points but immense prestige.
Realm First! Fall of the Lich King: Awarded for the server's first 25-player Heroic defeat of the Lich King.
Shadowmourne Achievement: Awarded for completing the lengthy questline to obtain the legendary axe.
Invincible's Reins: Awarded upon obtaining the extremely rare drop of the Lich King's personal mount.
Sources : Noobtoboss - Wowhead