Wanted to make a straightforward and comprehensive guide for this achievement because it can be annoying if you dont know exactly whats up with this one.
There are checkpoints the game checks for after you go through the Omega-4 Relay, the Tartarus Debris Field, the Collector Base, and the Hold the Line sections.
i modeled this solution off of the Mass Effect Wiki and ign website with my own personal injections.
Tartarus Debris Field
Silas Armor Check
This happens when the Oculus lasers attack your ship and checks if you have upgraded this at the Normandy upgrade center.
If you did upgrade this, then Jack will live.
If you did not upgrade this, then Jack will not live.
Cyclonic Shield Check
The next check is whether you upgraded the Normandy's shields.
If you did upgrade this at the station, nobody will die.
If you didnt, a squad member will die, in this order:
Kasumi > Legion > Tali > Thane > Garrus > Zaeed > Grunt
The order will change based on who you have recruited and have taken with you into the shuttle bay. (If you didnt upgrade the shields and want a specific member to survive, put them in your squad to make sure they surive this part).
Thanix Cannon Check
The third and last checkpoint for this section is for the heavy cannon upgrade.
If you did upgrade this option, everyone survives this part.
If you didnt upgrade, someone will die in this priority order:
Thane > Garrus > Zaeed > Grunt > Jack > Samara / Morinth.
Since this takes place right after the cargo bay fight, theres no way to protect any unloyal squad members with this one.
Collector Base
Vent Specialist
The first option inside the base you are faced with is picking a vent specialist to go alone, and also a second fireteam leader. You'll NEED to pick a loyal squad member for them to live. if you dont, they will die at the end. It is only the person who you pick as the Vent Specialist who will be at risk of dying here.
For the Vent Specialist, you should pick a Loyal Tali, Loyal Legion or Loyal Kasumi.
For the Fireteam Leader, you should pick a Loyal Miranda, Loyal Jacob or Loyal Garrus.
If you fail to pass even one of the above checks, the Vent Specialist will die.
you need to pick a tech expert as the Vent Specialist since only they can pull off the vent task. Additionally, the Fireteam Leader needs to be someone with experience leading a team. However, even if you meet the above requirements, if either the Vent Specialist or the Fireteam Leader are NOT Loyal, the Vent Specialist will die.
(i personally chose a loyal Tali for the vent and Jacob for the second team leader).
Normandy Crew
After this section you meet the Normandy Crew, the one part i found particuarly frustrating in the design of the game. According to Game Informer, how many missions you did before lauching this one determines whos left alive.
If you did zero Missions / Assignments and went through the Omega-4 Relay as soon as possible, all of the crew will survive.
If you did 1-3 Missions / Assignments after the crew were kidnapped, half of the crew will die, including Kelly, Gabby, Ken, and Mess Sergant Gardner .
If you did 4 or more Missions / Assignments after the crew were kidnapped, all of them except Dr. Chakwas will die.
I personally wasnt able to find a way in my playthrough to have all loyal squad members and immediately go into the suicide mission to save the entire crew, so perhaps do Tali's loyalty mission as soon as it becomes available as i put hers off till the end.
Long Biotic Walk and Second Fireteam
At this point you will split into two teams, and you will need to choose a Biotic Specialist and a leader for the second fireteam.
For the biotic specialist
If you pick a Loyal Jack, Samara or Morinth, your team will survive.
If your pick is anyone else, and/or Disloyal, then a member of your accompanying squad will die, in the following order of priority:
Thane > Jack > Garrus > Legion > Grunt > Samara > Jacob > Mordin > Tali > Kasumi > Zaeed > Morinth.
(for some reason i found out Miranda isnt capable of doing this part, even though she claims she can so i wouldnt pick her).
Second Fireteam Leader
This works similar to the Vent Specialist section.
If you pick a Loyal Miranda, Loyal Jacob or Loyal Garrus, they will survive.
If you pick anyone else, or somebody not Loyal, they will die.
However this time, it would be person directly who you pick who is in risk of dying if they arent Loyal.
Crew Escort
If you choose somebody Loyal to escort the crew, both the escort and the crew will survive.
If you choose somebody Disloyal to escort the crew, the escort will die but the crew survives.
If you DON'T decide to give the crew an escort, the crew will die.
If strong characters like Grunt, Garrus or Zaeed have died before this point, you'll want to avoid sending another strong character as the Escort here as that may negatively affect the outcome of the Hold the Line section.
(i personally chose a loyal Kasumi for this).
(Note: The Crew Escort section here is NOT necessarily for this particular achievement. If the crew happens to die, you can still get the achievement. i just personally like to save as many people as I can).
Finale
The last actual decision you need to make is who will accompany you and who will hold the line in the endgame here. This first decision is easy.
If a Squad Mate you take with you is Loyal, they will live.
If a Squad Mate you take with you is NOT Loyal, they will die.
Holding the line
This part was easily the most annoying to try and figure out. This section is calculated differently from all the other sections for some reason.
Essentially, whether a squad member lives or dies is determined by an average Point value determined on who makes up the group, and whether or not they are loyal. Here are the base point values of your Squad Mates:
4 Points: Grunt, Zaeed, Garrus
2 Points: Thane, Legion, Jacob, Miranda, Samara / Morinth
1 Point: Jack, Kasumi, Tali, Mordin
If any squad member is not Loyal, their point value is reduced by 1.
The average number of Points the team has will determine how many of them die. If the average is above 2, everyone on the team will live. Anything below that will risk up to three party members dying.
While the exact requirements will vary, in general an average of 1.5 will result in one death, an average of 1 will get two deaths, and an average of 0.5 - 0 will get three deaths. This means that if four or more characters are left to Hold the Line, it's impossible to have all of them die.
The pecking order of deaths is:
Mordin > Tali > Kasumi > Jack > Miranda > Jacob > Garrus > Samara / Morinth > Legion > Thane > Zaeed > Grunt
Because deaths caculated on the team's average Point value, a smaller team can still survive if strong characters are present. For example, Grunt can survive entirely on his own because even his Disloyal point value is 3. Having a Disloyal Tali with Grunt will still result in both of them living, because the team's Point average will be 2.
Basically the more loyal squad members you have, the better youll be in this section.
If Shepard Lives
The final check in the Suicide Mission is at Shepard's jump towards the Normandy.
If 2 or more squad mates have survived, Shepard successfully makes the jump and will live.
If 1 or 0 squad mates have survived, Shepard doesn't make the jump and will die.
Best of luck to you and upvote if this is straightforward and helpful :)