The stiff rules of Exercise in Fertility I got. Miserably, but I got it. And I think the rules apply to Head of the Family as well, but I've been trying for years.
1. Once you move in to your home, you can't change it. You can't buy another property and move to it, and you can't go visit Egypt (etc).
2. I did EiF by having a couple raise all 15 children personally: lots of birthday cakes (and counters to put them on), and moving the children out as soon as there was a young adult who could move.
3. Adoptions did not count, but children taken away by the social worker did. I had 9 total children removed, because if one gets unhappy, the worker takes all minors.
---It was really dumb: so many kids crying, that the babysitter didn't even get into the house because she was covering her ears during her time... and so they didn't get cared for.
4. Money cheats were okay. It helped to not have a job, but I think I did get somewhat permanent maternity leave. It takes a full day after conception before leave starts, and two days after birth before you have to go to work again. At some point, you'll be planning to use the ordinary days off too to get it done.
5. You don't have to raise them well, waiting until they're potty trained and walking/talking, or an honor roll student, or even well fed and happy before a birthday... and they can have a birthday each day - before midnight and just after, taking one cake each time.
Somewhere I learned that the Head of the Family achievement requires a female grandparent.
I also learned somewhere that ordinary Sims3 achievements require not being Supernatural - no fairy grandmothers, ghost daddies, vampire mommies, or genie babies.
I assumed 'no changing your household' meant I couldn't make a Simbot to help out, hire a butler, or buying the Bonehilda either. I made it simple by not having even minor pets.
I figured out that the computer prefers to balance the genders, so deleting all the random Sims that are in town and replacing them only with single custom females in their own home was a bust. Just to be safe, I didn't Edit Town after moving the main family in.
Your baby's mama doesn't need cribs, but it's helpful to have a shower and double bed.
Your reputation doesn't matter, as I have seven sons (and their mother) each with one woman with a total of 32 children and still no achievement. But waiting for them to forgive and forget your cheating ways can take too much time, I suppose, and I didn't seem to have the problem, but shouldn't it make a new gal less likely to trust you?
I set up 8 custom Sims, with an elder mother and seven sons who all had
...Family Oriented (because you can choose Try for a Baby from Special) and
...Hopeless Romantic (because it has more options for getting the gal to like you) and
...Friendly (Get to Know) and
...Flirty and just so they had something to do, Bookworm.
I had custom gal Sims with the same attributes, each in their own home, and 'raised' til they had Fertility Treatment. Then I saved them, moved them into a new town and moved the men into town too, but.... It didn't work.
I had one set up with all the girls and the main household with just a mom and her son... one of the girls homes was a mother and daughter (adult and teen)... and I gave a cake to the teen and got them both pregnant simultaneously... but they weren't even suspicious of cheating... and I got them both pregnant a second time and stopped paying attention to them altogether. This achievement has my Sims doing some very insensitive things. I want it done.