This is a lot simpler than it initially seems, but will take some paying attention and dedication.
At the start of the game, write down the last names of the people in your vanguard. If you get any siblings among the people in the first battle, restart since you want five unique bloodlines. As soon as you can, build five keeps, and appoint one person from each family to them. Make sure these keeps are not in outlying areas of the map, as this will put them at great risk late-game. Now you'll want to make sure that throughout the entire game, at least three of these bloodlines survive all the way to the end. Feel free to crossbreed between the families, as it's only the surname of the ruler that matters in deciding the babies' names. Babies adopted into a keep also become part of that bloodline, so feel free to use that function if any family is lacking members. When appointing new rulers and partners for them, always seek to have the highest fertility rate possible to ensure a lot of members of each family are around at all times.
Lastly, when appointing Sagewrights and Standards, don't use people from families with small numbers. Your top priority is always to keep the bloodlines going. When it's time for the final battle, make sure your vanguard consists of heroes from at least three of the original families. The achievement pops at the start of the fight.
If you're just starting the game and this sounds confusing, don't worry. The tutorials explain all these things just fine.