AbsolutioN IX & FayMoon have pointed out in the comments you can unlock this achievement and "Monarch Abides" in a single playthrough with a carefully timed manual save.
At any moment during this mission, you can SAVE the game and decide to give the targeting module to Sanjar, Graham or Zora, win the battle for selected faction and get the alternative achievement "Monarch Abides". Then reload back and finish "Canid's Cradle" with peace solution to unlock "Peace in Our Time" achievement.
Also, for this achievement, you will need to make sure you complete the optional opjectives "wipe the terminals" for Sanjar and choose food supplies / save the Van Noys (Graham / Zora), during their respective quests.
-------------------------------------------------The following solution was taken from PowerPyx's trophy guide - full credit to PowerPyx.
This trophy and Monarch Abides are mutually exclusive, you can’t do them both in the same playthrough without using save backups.
For this trophy after you’ve stopped the radio transmissions and got the info sent to Phineas or talked Hiram into working for the board a UDL ship will crash into the planet. Go get the targeting module, then you need to talk Sanjar and Zora into working with each other for their own best interests.
To have the Iconoclasts agree you need to have Zora overthrow Graham. To allow this to happen in the two prior quests you do for the Iconoclasts you need to side with what Zora wants, getting the extra food supplies from the smuggler, then getting the Twins back from the press instead of having them go in and help you. After that once you have got the targeting module you can speak to her again and she’ll ask you to get some mission logs, which leads to the discovery that Graham orchestrated the pirate attacks. You then need to agree with her to overthrow Graham and kill him. You can then talk Zora into potentially working with Sanjar if you have 55 Persuasion, or other skills around that level.
Sanjar can then be talked into working with Zora if you find her report from the Rizzo’s Lab in the same area you get the items for Sublight. You then talk them into meeting at the OSI church just outside the city, where you can basically give mostly neutral and encouraging answers to have them talk it out and agree to work together. Once they do you’ll complete the quest and earn this trophy.