1. Start as William the Bastard de Normandie in 1066 - The Fate of England. Make sure to have Ironman enabled.
2. Raise your Crown Authority to 2 so you can revoke titles later on.
3. Assign some better vassals to your council and start swaying your Bishop for a few extra men.
4. You start the game at war with the King of England and you have an additional army of 4400 soldiers (Duke William's Host) available in Normandy (Northern France). Make sure to also raise your own levies and knights after unpausing the game for a few seconds.
5. Unfortunately Englands army is bigger than yours so you will need to use terrain to your advantage, hire some mercenaries or Men-at-arms and/or find some powerful allies. The latter can easily be achieved by marrying your children off. Select "Alliance Power" for sorting. You don't need to check "matrilinear" for your daughters because you don't want to play longer than a few years.
6. With the help of your new allies win the war against England. I attacked their capital Londres first, then conquered some counties around there, keeping my armies close together for the frequent clashes with the English forces.
7. After winning the war move your realm capital to any city in the Kingdom of England. Londres is a safe option.
8. Do NOT use the "Embrace English Culture" decision just yet. The discription clearly states that only Norman or French vassals (in England) will convert to the English culture with you. However, most of your vassals in England will be Anglo-Saxon or even Scots. You need to get rid of them first. You will also be way above your domain limit, but resist the urge to give your counties away.
9. First deploy your armies because you will likely have to fight. Then one by one imprison your non-Norman vassals and then revoke their titles. I didn't check if they were in England and I also revoked the Barony titles to be sure. Some of them will resist arrest and force you into a war.
10. Once you win the war you will have imprisoned those rebellious vassals and can revoke their titles. That in turn gains you new non-Norman vassals which had been vassals to the Dukes you just got rid of and which you should now also dispossess.
11. When you are done, let the game continue for a few seconds, then check back in the vassals list if any non-norman vassals remain.
12. Once you're sure to have only Norman (or French) vassals take the "Embrace English Culture" decision. The achievement should unlock as soon as you let the game continue.
You will want to finish the process within William's lifetime. Some players have reported the achievement not unlocking for any of his heirs even after meeting all the requirements. I also encountered that issue myself.
William is a powerful Commander, so not using him to command your army is a tough choice. Losing him in battle might be worse though.