This achievement is slightly confusing at first glance but thats only because Centrist isn't one of the trackable stats in your officer profile. The stat you are looking to track is Moralist and you will receive a point towards it every time you answer in a neutral way when a political question is asked. Moralism is a political stance that supports the system/government and believes in progress through steady and slow change.
You might need to wait until day 3, when you have access to the fishing village, to have enough opportunities to get this, but keep an eye out for any kind of answers that sound like "I don't have an opinion about this either way" when asked about the strike, the Revolution, or people's political beliefs. The idea is to stay toward the moral "center" or neutral about most political topics.
During conversations, choose replies that show that you are neutral, similar to what a cop should say on the job like, "I don't choose sides" or "I don't have an opinion about this thought/topic."
*Spoilers below* I did not list every possible conversation where you have an opportunity to get a point toward this achievement but there are a few listed below which are the ones that I used to unlock the achievement. You will get a chance to talk/support Moralist ideologies when you talk to Kim Kitsuragi, Joyce the Wild Pine lady, Evrart the union boss, Rene the old veteran, Gaston (Rene's friend), Lena (the cryptologist's wife), Sunday Friend, Titus Hardie, and Klassje among others. Do so several times until your Empathy starts a converstaion with you. You can also check how many points you have in the Task Menu after acquiring your Notebook/Ledger.
You should pick sentences like these:
When you talk to Rene (the old veteran in blue) and are asked to present your opinion, choose "This coalition seems quite capable."
When you inspect the yellow broken mug from the trash canister, choose "I'm going to use it as an example of what not to do."
When Joyce tells you about the union demands ("Every worker-- A member of the Board!"), say "I don't know what to think about it".
When you talk to Elizabeth (the gardener), ask her why she is so aggressive, then reply "I don't know where you heard that, but it's wrong. The RCM is principled and strong, unlike you socialists."
When you find a Communist magazine in the Harbor (the shack where Rene stands guard), choose "Why should I care? This doesn't have anything to do with me."
When Evrart gives you your first task, go to Call Me Manana and ask for the key, then say "I'm not doing this for political reasons."
Talk to Rene after you visit his guard booth and choose "There's absolutely nothing wrong with tare-collecting. It's my side-thing too."
When you meet Sunday Friend after talking to the man on the balcony, ask him about Sur-la-clef and reply "It's like every time I'm talking to people I'm choosing option D, none of the above... Is that moralism?"
During the debriefing with Kim at the end of the day, ask about the Moralintern and reply in your conclusion, "On second thought, I don't have an opinion. Forget about it."
*Very important* Remember that, more often than not, you can replay conversations and choose a different answer, which will still count towards your total.
As part of completing this trophy, you'll also complete the opening steps for earning the Committee of la Responsabilité achievement.