As far as I can see, no one else has published a complete guide anywhere explaining how to get all of the achievements in Company of Heroes 3, so I figured I would take a shot at it as I found many of the default achievement descriptions, particularly for the campaign, to be rather vague.

This guide is very much still a work-in-progress, but I intend to finish it completely soon.

It Always Leads Me Here
Win a Multiplayer or Skirmish match

Winning a match in any of the following modes will count:

• Quick Match
  
• Co-op VS AI
  
• Skirmish

But Still They Lead Me Back
Win 25 Multiplayer or Skirmish matches

Same as above. Any mix of 25 wins will count as it is totaled cumulatively.


You're Missing The Point
Complete a Mission or Skirmish without reinforcing a Squad

To finish a match without reinforcing any squads, simply do not retreat any of your squads to your HQ when they suffer casualties for an entire match. Also, make sure to stay away from all reinforcing units like ambulances, medical bunkers, and hospitals (if in campaign) as well.

Can only be unlocked in single player game modes.


0k
Complete a Mission or Skirmish without losing a Squad

To finish a match without losing any squads, frequently utilize healing, reinforcement, and retreating. If a squad loses all of its men, or is forced into a rout (such as team weapons), then this will count as a squad lost.

If you're struggling to do this, you can just play a 4v4 in Skirmish and put your team's AI on Expert and the opposing team's AI on Easy and let your team finish the match.

Can only be unlocked in single player game modes.


No Quarter
Win a Multiplayer or Skirmish match without losing a Victory Point ticket

To finish a match without losing a single Victory Point ticket, secure and maintain a majority of the Victory Points for the entirety of the match. You can lose and regain any number of Victory Points, but as long as you hold more than 50% of all Victory Points for the entire match you will not lose a Victory Point ticket.

If you're struggling to do this, you can just play a 4v4 in Skirmish and put your team's AI on Expert and the opposing team's AI on Easy and rush all of the map's Victory Points and guard them for the entire match.


Full Stop
Issue an order in Tactical Pause

To issue a Tactical Pause, simply press 'Spacebar' in any single player game mode and queue up an order for any of your units. Tactical Pause freezes time in-game and you will be able to queue up many actions for all your units, and then press 'Spacebar' to unfreeze.


Master Of Full Stops
Issue 500 orders in Tactical Pause

Same as above; simply issue 500 different orders to your units across all single player game modes.


Company Commander V3
Use Battlegroup Abilities 100 times

Use any Battlegroup Abilities 100 times cumulatively across all game modes.

Battlegroups with multiple cooldown abilities will be faster, such as US Airborne or UK Air and Sea.

El Alamost
Complete the North Africa Operation

The North Africa Operation contains 8 levels, complete them all on any difficulty:

• Ajdabiya Assault
  
• Fire With Fire
  
• Gazala's Cauldron
  
• The Fox's Trap
  
• Signals Crossed
  
• The Fall of Tobruk
  
• Scorched Sand
  
• The Battle of El Alamein

Note that once you start the campaign, you will not be able to adjust the difficulty without starting over from the beginning.

The First Step
Complete Mission Zero

Finish the tutorial for the Italian campaign.


The Second Step
Complete Calabria

Finish the campaign objective "Push North and Secure Calabria" by capturing the city of Catanzaro.



The Way Forward
Decide where to go after Salerno

Finish the campaign objective "Secure a Beachhead" by capturing the port city of Salerno.


Volturno Breaker
Break the Volturno Line

Finish the campaign objective "Break The Volturno Line" by capturing the following cities:

• Cancello
  
• Caiazzo
  
• Campobasso
  
• Termoli

Historical Reparation
Save Monte Cassino

Capture the city of Monte Cassino.


Gustav Breaker
Break the Gustav Line

Finish the campaign objective "Break the Gustav Line" by capturing Monte Cassino (same as above).


Anniehilator
Silence Anzio Annie

Capture the port city of Anzio.


Hot Dog!
Complete the Italy Campaign

Finish the campaign objective "Break The Winter Line" by capturing one of the following cities:

• Velletri
  
• Palestrina
  
• Subiaco

Lest We Forget
Collect all Soldier Stories

Soldier Stories are the journal entries shown on the loading screens before and after unique missions and skirmishes when capturing cities. To unlock them all, simply capture all of the cities in Italy before breaching any part of the Winter line (which consists of the following cities):

• Vellestri
  
• Palestrina
  
• Sabaco

Fan Of Support
Purchase a Detachment

On the campaign map select your Battleship and then in the bottom right, select the detachment menu.

Purchase and deploy any of the following company detachments from the ship.

• US Airborne
  
• US Special Forces
  
• US Armored
  
• UK Indian Artillery
  
• UK Armoured Support
  
• UK Air and Sea

Gung Ho
Gain 100% loyalty with Buckram

You primarily gain loyalty with General Buckram by conducting bombing raids with B-25 Mitchell Bombers (infinitely repeatable) and by capturing airfields. Buckram will occasionally ask you to complete time-limited objectives and if you do them you will gain loyalty and if you do not do them you will lose loyalty. Will be granted once you reach 100%.

Buckram's loyalty provides the following rewards:
20% - "Logistics Chain"
Delivered supply shipments grant an additional +35 fuel.
40% - "Advanced Landing Fields"
Awards 60 munitions for destroying an emplacement with a bomber.
60% - "Airborne Reinforcement"
Removes the cooldown time on the Airborne Company's Heal Target ability.
80% - "Marston Mats"
Decreases the fuel and munitions cost of all aircraft abilities by 20%.
100% - "Buckram's Loyalty"
Ensures Buckram's support in your final offensive to break the Winter Line.


Slow And Steady
Gain 100% loyalty with Norton

You primarily gain loyalty with General Norton by capturing ports and supply depots. Norton will occasionally ask you to complete time-limited objectives and if you do them you will gain loyalty and if you do not do them you will lose loyalty. Will be granted once you reach 100%.

Norton's loyalty provides the following rewards:
20% - "Navigator"
Increases the movement range of all naval vessels and allows them to be repaired away from seaports.
40% - "Boot Camp"
All newly trained units start with 5 skill points.
60% - "Training Manual"
Doubles veterancy gain rate for companies that are veterancy 0 or 1.
80% - "Expert Generals"
Veterancy 3 units transfer veterancy to closet nearby company.
100% - "Norton's Loyalty"
Ensures Norton's support in your final offensive to break the Winter Line.


Terra Nostra
Gain 100% loyalty with Valenti

You primarily gain loyalty with Eleonora Valenti by using partisan abilities (infinitely repeatable) and by capturing partisan hubs and hospitals. Valenti will occasionally ask you to complete time-limited objectives and if you do them you will gain loyalty and if you do not do them you will lose loyalty. Will be granted once you reach 100%.

Valenti's loyalty provides the following rewards:
20% - "Local Relations"
Improves the Capture Target ability at partisan hubs, giving it a high chance to double its effect each turn.
40% - "Civilian Intel"
Reveals enemy locations along the frontline, showing companies and detachments near each town, depot, and airfield.
60% - "Enigma Decrypts"
Reveals enemy company, airfield, and naval actions.
80% - "Captured Materiel"
Improves the Loot Target ability at partisan hubs, doubling the resource reward for looting enemy locations.
100% - "Valenti's Loyalty"
Ensures Valenti's support in your final offensive to break the Winter Line.


Sweet Victory
Heal a unit with ice cream

1.) Capture the port city of Barletta (it is northwest of Bari along the southeast Italian coastline). Keep a partially damaged unit near the city.

2.) Transport or produce a battleship and station it to the buoy just outside of the city. Leave the battleship stationed there until you are done.

3.) End your turn and you will get the following dialogue from Corporal Joe Conti:

Originally posted by Corporal Joe Cont:

If I could speak with you for a moment, Commander. The men... well they're tired. But I know a guy who might be able to help. If you could convince the Navy to bring one of their ships to Barletta, he can rustle us up some ice cream. I think the men'd really appreciate it.

4.) End your turn again and you will get the following dialogue from General Norton:

Originally posted by General Norton:

Sir. I'm told the Americans intend to provide ice cream for their troops. I really don't see the value in such frivolous actions.

5.) End your turn again and you will get the following dialogue from Corporal Joe Conti:

Originally posted by Corporal Joe Conti:

Okay, men. Thanks to our theatre commander, I've lined up some delicious ice cold treats for everyone on leave at Barletta. Get 'em while they're cold.

6.) Move any partially damaged unit into the city of Barletta and you will get the following dialogue from Corporal Joe Conti:

Originally posted by Corporal Joe Conti:

There we go, men. Ice cream all around.

7. End your turn and you will get the achievement. You can now heal at Barletta whenever you end your turn with units garrisoned there.


The Cover-up
Uncover a conspiracy

Please refer to KyariRhyZan's comment below or Wojtrox's Steam guide on the matter until I get around to testing and writing this one out myself.