Mass Effect

Do as few missions and assignments as possible until your search for information on Saren points you to the Med Clinic in the Ward. This occurs after you leave the Normandy for the first time, talk with Udina and the captain, then travel to Chora's Den.

When you arrive at the Med Clinic, there will be a battle and after that you choose to let Garrus into your party. Keep him in your party throughout all missions and assignments. For optimal effect, choose a character that is stronger in assault or casting depending on your character class. Garrus is strong in electronics, so I don't recommend choosing Tali, the quarian.

For missions see http://masseffect.wikia.com/wiki/Missions. For assignments, see http://masseffect.wikia.com/wiki/Assignments.

You need to do all the missions. While most of these open up automatically throughout the story line, there is one tricky one that you have to hunt for first: Novario: Quarantine (http://masseffect.wikia.com/wiki/Mass_Effect_Guide#Rift_Stat...). To get this, find Dr. Zen Cohen in the medical bay at Rift Station on Novaria and talk to him about a cure. Do this mission.

You'll need to complete around 40-45 assignments with Garrus in your party. If you fly through the missions, make a game save right before leaving the Citadel for Ilos and play a bunch of assignments to be sure. Once you leave for Ilos you're pretty much stuck with finishing the main story line. With the game save before leaving for Ilos, you can at least reload it and do more assignments if you decide to finish the campain. Just don't overwrite it accidentally or you'll have to start a new play through.

According to Mass Effect Wiki, you unlock this achievement by completing 50 assignments with Garrus 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) I suggest using Liara as your extra character when going for this achievement. She is the only other character who needs 50 assignments complete, so you should unlock both at the same time.
4) When you earn this, all characters will have recharge time on Damping and Overload reduced by 10%

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

To get this achievement is really easy. Once you recruit Garrus into your party put him in your party when you go on missions. He has light/medium turian armor. He can use a pistol,assault rifle and a sniper rifle. With him he's good at combat and tech so use to take out enemies shields and weapons. He can also hack and boost your mako shields as well.

He makes taking out any group of bad guys easier he also works well with Wrex and Kaiden. You need to do at least 40-50 missions and the achievement should unlock.

Class: Turian Agent
Assault Rifles
Sniper Rifles Unlocked at Assault Rifles 6
Tactical Armor Can use Turian Light and Turian Medium Armor
Assault Training Unlocked at Tactical Armor 5
Decryption
Damping Unlocked at Decryption 4
First Aid
Electronics Unlocked at First Aid 7

(FYI- I used the mass effect wiki)
http://masseffect.wikia.com/wiki/Garrus_Vakarian
(before you give me a "thumbs down" on this or any other solution. Tell what I can do to fix it)

I don't know about the others but I needed all together 54. I did excel sheet and cross it every time I did assignments or mission. I took the list of assignments and missions from:
http://masseffect.wikia.com/wiki/Assignments
http://masseffect.wikia.com/wiki/Missions

The moment I first got in Citadel and got the missions I did the Gerrus one. Since them I had him in my team all the time. Till the moment I went to Noveria I had about 32 assignments and 3 mission (if you count the Wrex and expose Saren mission in Citadel). Then I did Novaria and Feros.
According to Mass Effect Wiki Gerrus achievement needs 50 assignments. If that would be correct I would get achievement when I finished one of the side mission on Feros but it didn't. I got it when I destroy Geth ship.

I don't know if this is really a solution maybe just a note how and where I got achievement.
Maybe the first mission on Citadel doesn't count or maybe assignments UNC: Missing Marines ? UNC: Cerberus ? UNC: Hades' Dogs count as one even thought you have 3 listen in mission computer.

I obtained this achievement after completing 46 assignments and then beating the game. In that order. I got frustrated with trying to get this to pop and after assignment 46 I figured, screw it- I'll just beat the game. Right before fighting Saren (for the last time) achievement popped.