This achievement is obtained when you move into Class-5 apartment.

Update tips
Others have reported that you can get the achievement even if your family dies (as long as at least one of them survives). So if you want to do that, well, you can and it will likely be even easier.

The rest of this guide assumes you have your full family with you the whole time and you're playing on Normal mode. However, you can get this achievement also in Easy mode (thank you for the comments that confirmed this!), which makes it even easier. Check the comments for some interesting strategies by other people!

When you begin at your new job, you are assigned a class-8 apartment with a rent of 20 $ and heating cost of 10 $. You also have to eat for 25 $ per day (5 $ per family member). Rent will go up by 5 $ in a few days.

It costs 100 $ to move into each better appartment. So, to finally move to a class-5 apartment it will cost you a total of 300 $.

Here's a table of living costs in different classes of apartments:


You see that the living costs will go up by 5 $ / day every time you move. Moving as soon as possible will mean that you'll have to cover 95 $ in additional living expenses before you move into your class-5 apartment. That's almost 400 $ of extra expenses. This is of course assuming none of your family members die along the way.

Hint: You don't necessarily need to move as soon as possible. Opportunities to move will raise later. This will save you few tens of dollars.

Last section found that you need a bit short of 400 $ extra cash to move into a class-5 apartment. It turns out you don't need to do a perfect job to attain that, though it might help.

Premise: Notice how much food and heating costs? 25 $ for food and (initially) 10 $ for heating each day. Also notice that once you go hungry or cold, it won't affect your family immediately but usually only if this goes on for a longer time. Only your son will get sick for being hungry for a day. Let's use this information:

Alternate between not paying for food and not paying for heating.

Start by not paying for food after your first day. You'll save 25 $, though next day you'll have to pay 5 $ for your son's medicine while not paying for heating. This way, you will save 30 $ every two days.

After 12 days (when the first upgrade to class-7 apartment becomes available) you have already saved 180 $. Continue this practice throughout the game, always buying food only when hungry and the heating only when cold.

Here are some basic tips that are also useful, though not the main trick, to this strategy:

• Obviously, do a good job. This way you'll get more money.
  
• You are allowed to do two mistakes each day. Use this allowance to let two additional people through because you'll only get paid for the people who go through. Save this preferably for the last people of the day so you can take bribes without punishment before.
  
• Detain all the people you can once you can get a reward for it.
  
• Accept all the bribes you are offered at the post.
  
• Don't miss any shots.

With this strategy, in addition to moving to a class-5 apartment you can even buy all the upgrades and be all goody-goody if you'd like, assuming you're already good at your virtual job.

I'll share here what my Day 24 (the day of the final move to class-5 apartment) looked like after using this strategy for the whole game:



Hopefully you found this guide useful. Also, any suggestions on additional information to add will be appreciated.