Mass Effect

According to Mass Effect Wiki, you unlock this achievement by completing 45 assignments with Wrex out of the disc's 73. Each DLC adds 3 to that list, making for a max of 79.

1) You do not need the character in your party to count toward your total, you just need him there when the assignment is marked "completed"
2) YES, DLC assignments can count, and are much easier than some in game assignments.
3) It make little difference who you use as your other character, as all the other characters need 45 assignments complete, save Liara who needs 50 assignments. Pick the squadmate who seems ideal for the situation or who will compliment your squad best.
4) When you earn this, all characters will regenerate 1HP per second no matter what.

ACHIEVEMENTS
http://masseffect.wikia.com/wiki/Achievements#Squadmates
ASSIGNMENTS
http://masseffect.wikia.com/wiki/Assignments

I kept track of achievements and missions completed with my part of Tali and Wrex. I tracked how much EXP was given for the completion of each assignment and mission. It seems Tali's achievement unlocked after I had 75000 EXP earned from missions/achs during her stay in my party. Wrex's achievement came as soon as I completed Feros, Tali's came after I gave Gavin Hossle his data (right before beating the Thorian). The top half of the list is a summary, there is a bit more detail below.

Total number of missions: 11
Total number of assignments: 28
Total EXP earned from completed missions: 18250
Total EXP earned from completed assignments: 53700
Total EXP earned from completed missions/assignments: 72950
(Wrex's ach came after earning 7000 EXP after beating the Thorian, so it was from the first thing I did after earning Tali's)

Missions

Completed Before: (4)
Prologue: Find the Beacon
Citadel: Garrus
Citadel: Wrex
Citadel: Expose Saren

Open Before: (1)
Citadel: Expose Saren

Completed With: (11) - 25250 (18250 for Tali, the last 7000 was earned when I finished Feros and got the Wrex ally achievement)
Citadel: Expose Saren - 5000
Feros: Colony Saved - 11500
Noveria: Matriarch Benezia - 2000
Noveria: Leave Port Hanshan - 1500
Noveria: Lorik Qui'in - 1500
Noveria: Peak 15 - 1500
Noveria: Reactor Repair - 0
Noveria: Reconnect Landlines - 1000
Noveria: Contamination - 1500
Noveria: The Hot Labs - 1500
Noveria: Rift Station - 750

Open When Achievement Came: (0)
Find Liara T'Soni

Assignments

Completed Before: (0)

Open Before: (1)
Citadel: Reporter's Request

Completed With: (28) - 53700
Citadel: Reporter's Request - 1000
Citadel: Jahleed Returns Mateials - 2000
Citadel: Homecoming - 1000
Citadel: Presidium Prophet - 1000
Citadel: Asari Consort - 1000
Citadel: Rita's Sister is Safe - 1500
Citadel: Xeltan Convinced - 100
Citadel: Scan the Keepers - 2100
Citadel: Doctor Michel is Safe - 1000
Citadel: Schells has his Data - 1000
Citadel: Signal Tracking - 3000
X57: Bring Down the Sky - 3000
X57: Missing Engineers - 1000
X57: Avoid the Blasting Caps - ?
Pinnacle Station: Combat Missions - 19500
Pinnacle Station: Vidinos - ?
Pinnacle Station: Convoy - ? (0?)
Noveria: Espionage - 1500
Noveria: Smuggling - 1000
Citadel: The Fourth Estate - 1100
Citadel: Planting a bug - 1500
Citadel: Family Matter - 1000
Citadel: Old Friends - 3000
Feros: Geth in the Tunnels - 1500
Feros: Water Restoration - 1000
Feros: Varren Meat - 1000
Feros: Power Cells - 1000
Feros: Data Recovery - 1000

Open When Achievement Came: (15)
UNC: Missing Survey Team
UNC: Missing Marines
UNC: Privateers
UNC: Hostile Takeover
Citadel: The Fan
Unusual Readings
Strange Transmission
UNC: Hostage
UNC: Rogue VI
Doctor at Risk
Mercenaries
UNC: Beseiged Base
UNC: The Negotiation
Investigate Shipments
Investigate Samples





Missions

Completed Before:
Prologue: Find the Beacon
Speak to the Captain
Head to the Dig Site
Investigate Research Camp
Take the Train
Speak to Joker
Complete

Citadel: Garrus
Speak to Harkin
Go to the Med Clinic
Complete

Citadel: Wrex
Go see Barla Von
Speak to Wrex
Copmlete

Citadel: Expose Saren
Go to the Tower
Investigate Saren
Take Down Fist
Save the Quarian

Open Before:
Citadel: Expose Saren
Return to the Tower

Completed With:
Citadel: Expose Saren - 6670
Return to the Tower
Speak to the Ambassador
Complete

Feros: Colony Saved - 11500
Go to Feros
Speak with Fai Dan
Stop Geth in Tower
Inform Fai Dan
Get to ExoGeni Headquarters
Investigate Mysterious Signal
Investigate ExoGeni Headquarters
Remove Force Field
Destory Geth Ship Claws
Exit Exo GeniSpeak with Refugees
Return to Zhu's Hope
Return to Zhu's Hope
Minimize Casualties
Destroy the Thorian
Complete

Noveria: Matriarch Benezia - 2000
Go to Noveria
To Peak 15
To Rift Station
To the Hot Labs
Back to Rift Station
Mission Complete
Complete

Noveria: Leave Port Hanshan - 1500
Administrator Anoleis
A Stumbling Block
A Garage Pass
Complete

Noveria: Lorik Qui'in - 1500
Speak to Lorik Qui'in
Lorik's Dilemma
Break-In
Evidence in Hand
Gianna
Gianna's Proposal
Lorik Agres
Complete

Noveria: Peak 15 - 1500
Mysterious Rumors
Computers Damaged
Complete

Noveria: Reactor Repair - 0
Reconnect Fuel Lines
Complete

Noveria: Reconnect Landlines - 1000
Reconnect Landlines
Complete

Noveria: Contamination - 1500
Clear the Chamber
Complete

Noveria: The Hot Labs - 1500
Arm the Purge
The Pass Card
Acquired Codes
Purge Armed
Code Omega
Complete

Noveria: Rift Station - 750
Sneaking In
Breaking In
Complete

Open When Achievement Came:
Find Liara T'Soni
Go To Artemis Tau

Assignments

Completed Before:

Open Before:
Citadel: Reporter's Request
Deliver OSD

Completed With:
Citadel: Reporter's Request - 1000
Deliver OSD
Look for Information
Complete

Citadel: Jahleed Returns Mateials - 2000
Speak with Jahleed
Talk to Chorban
Talk to Jahleed
Complete

Citadel: Homecoming - 1000
Talk with Diplomat
Inform Mr. Bhatia
Complete

Citadel: Presidium Prophet - 1000
Speak with the C-Sec Officer
Resolve the Dispute
Inform the Hanar
Complete

Citadel: Asari Consort - 1000
Speak with Gen. Septimus
Speak with Sha'ira
Complete

Citadel: Rita's Sister is Safe - 1500
Speak with Rita
Talk to Jenna
Return to Rita
Talk to Chellick
TMake the Pickup
Return the Shipment to Chellick
Complete

Citadel: Xeltan Convinced - 100
Speak to Xeltan
Complete

Citadel: Scan the Keepers - 2100
Scan the Keepers
Complete

Citadel: Doctor Michel is Safe - 1000
Talk to Doctor Michel
Talk to Morlan
Talk to Doctor Michel
Complete

Citadel: Schells has his Data - 1000
Speak to Schells
Scan the Machines
Speak to Schells
Complete

Citadel: Signal Tracking - 3000
Track the Signal
Follow Signal to the Presidium
Continue Tracking
Complete

X57: Bring Down the Sky - 3000
Disable the Torches
Head to the Main Fascility
Deactivate teh Charges
Free the Hostages
Complete

X57: Missing Engineers - 1000
Missing Engineers
Foudn Body of Hymes
Foudn Body of Mendel
Found Body of Montoya
Complete

X57: Avoid the Blasting Caps - ?
Proceed On Foot
Complete

Pinnacle Station: Combat Missions - 19500
Talk to Ochren
Get top score in eight missions
Get top score in last four missions
Survive Ahren's Challenge
Complete

Pinnacle Station: Vidinos - ?
Beat Vidinos's Scores
Complete

Pinnacle Station: Convoy - ? (0?)
Travel to Intai'sei
Contact the Convoy
Complete

Noveria: Espionage - 1500
Keep him Talking
Hacking complete
Complete

Noveria: Smuggling - 1000
Retrieve the Packasge
Return the Package
Complete

Citadel: The Fourth Estate - 1100
Complete

Citadel: Planting a bug - 1500
Plant the Bugs
Copmpete

Citadel: Family Matter - 1000
Complete

Citadel: Old Friends - 3000
Find the Turian
Complete

Feros: Geth in the Tunnels - 1500
Find the Geth
Inform Fai Dan
Complete

Feros: Water Restoration - 1000
Find More Valves
Inform Zhu's Hope
Complete

Feros: Varren Meat - 1000
Inform Zhu's Hpe
Find Alpha Varren
Complete

Feros: Power Cells - 1000
Return Cells to Zhu's Hope
Find Cells
Complete

Feros: Data Recovery - 1000
Find the Console
Deliver OSD to Hossle
Complete

Open When Achievement Came:
UNC: Missing Survey Team
Find Missing Reesearchers

UNC: Missing Marines
Find Recon Team

UNC: Privateers
Go to the Strenuus System

UNC: Hostile Takeover
Eliminate Crimelords

Citadel: The Fan
Conrad Verner

Unusual Readings
Investigate System

Strange Transmission
Find the COmmune

UNC: Hostage
Board Freighter

UNC: Rogue VI
Engage VI

Doctor at Risk
Find the Doctor

Mercenaries
Investiage Mercenaries

UNC: Beseiged Base
Get to Medical Base

UNC: The Negotiation
Meet Darius

Investigate Shipments
Got to Amazon System

Investigate Samples
Go to System

You do not need to do 45 assignments!

The DLC seems to be worth more. I completed 11 missions and only 26 assignments when this popped, though 5 of my assignments were from X57 and Pinnacle Station.

For missions, I completed only Find Liara T'Soni and all of Noveria. While i started Feros I did not need to complete it. The Snorg's solution lists the mission titles if you need them.

For assignments I only completed 21 non-DLC, mostly Citadel assignments, the first four Feros assignments from the tunnels, and a few quick non-shooting assignments like UNC:Major Kyle or Noveria:Smuggling.

If you have the DLC, get those done first and the achievement will pop sooner!

!!!! READ THIS BEFORE USING WREX, IT COULD SAVE A LOT OF TIME! On Virmire there is a situation that will require you to have full charm or else . Resolving this situation will also give you the "Charismatic" achievement. I lost about 4 hours of gameplay due to this.