It should go without saying but I'm going to say it anyway: If you do not want to be spoiled on anything concerning Call of Duty: Advanced Warfare then you should probably not look at the complete list of achievements that I'm about to put below these words.
Carma
Kill an enemy by throwing a car door at them.

A New Era
Complete the campaign on any difficulty.

Hard Hitter
Complete the campaign on Hardened difficulty.

Excellence in Everything
Complete the campaign on Veteran difficulty.

Never Saw it Coming
Boost jump, dash forward, then air stomp on an enemy.

Escape Artist
Avoid 20 grenades by dodging with your exo.

Loud enough for you?
Kill 10 enemies or drones while affected by a sonic blast.

Maximum Overdrive
Kill 50 enemies while using Overdrive.

Genius
Kill 4 enemies with a single smart grenade.

Threat Detected
Paint 10 enemies with a single threat grenade.

Fly Swatter
Knock 25 Drones out of the sky with EMP grenades.

Where Are You Going?
Stop an AST with an EMP grenade.

History in the Making
Collect over half of the Intel.

Ferrum Absconsum
Collect all the Intel.

Riot Control
Kill 20 enemies while linked to the Mobile Cover Drone.

Advanced Soldier
Spend your first exo upgrade point.

Second Skin
Spend 10 exo upgrade points.

We Have the Technology
Spend 20 exo upgrade points.

Power Changes Everything
Completely upgrade your Exo.

Seoul Mates
Complete "Induction."

Not on my Watch
Prevent the walking tank from being destroyed by the Drone Swarm in "Induction."

Deadeye
Score "excellent" in the shooting range in "Atlas."

Grenadier
Score "excellent" in the grenade range in "Atlas."

Welcome to Atlas
Complete "Atlas."

Look Both Ways
Kill all the KVA in the traffic section without shooting a civilian vehicle in "Traffic."

Life in the Fast Lane
Complete "Traffic."

Fire and Forget
Kill 10 enemies with the Mobile Turret missiles in "Fission."

Radioactive
Complete "Fission."

Motor City
Complete "Aftermath."

Wheelman
Finish the hoverbike sequence without hitting any walls or obstacles or taking damage in "Aftermath".

Sitting Ducks
Kill 3 enemies with one shot of the Sniper Drone in "Manhunt."

Born to Die
Complete "Manhunt."

Betrayal
Complete "Utopia."

Party Crasher
Kill 20 enemies with the Grappling Hook in "Sentinel."

Crates on a Plane
Complete "Sentinel."

The Destroyer Returns
Complete "Crash."

Restricted Airspace
EMP 10 enemy aircraft out of the sky with the hovertank in "Bio Lab."

Irons in the Fire
Complete "Bio Lab."

GG
Complete "Collapse."

Man Overboard!
Melee an enemy so they fly off the side of the ship in "Armada."

Wrath of Atlas
Complete "Armada."

Flying Ace
Shoot down 10 enemies with machine guns in "Throttle."

Manticore Unleashed
Complete "Throttle."

Heavy-Handed
Go through 20 gun drops in one-armed combat in "Captured."

The Wheat from the Chaff
Complete "Captured."

Exo Survival Veteran
Play 50 Exo Survival Matches.

Exo Survivor
Successfully Complete Exo Survival Bonus Wave. Only attainable in Riot.

Class Warfare
Play 30 minutes with each class.

Exp Flip
Flip a map.

Flip Flop
Flip a map twice.

The list comes courtesy of IGN. For now, there are no point values assigned to the Achievements or Trophies, so they're left to your imagination for the time being.