A straightforward solution for this achievement is to make use of the Crusades mechanic.
Start in 1066 as the Karling Count of Vermandois and get to work fabricating on your neighbours, this will let you conquer them and build up your own strength. You’ll want to aim at creating the Duchy of Valois whilst upgrading your Men-at-Arms, definitely focus on siege weapons for this.
In the meantime get yourself and your brothers married, but DO NOT land your brothers. (N/B: It might take some time for the Crusade to pop and you’ll be playing as your Heir, but this will still work)
Eventually you’ll see the pop up saying the Pope now thinks Crusades are a great idea, wait for him to announce one for Jerusalem, commit to it and choose an unlanded family member as a beneficiary. Once the Crusade starts, call up your troops and make your way to the Holy Land. Best thing to do now is to wait in the sea for everyone else to land so you don’t instantly get stack wiped. Focus on sieging as the AI tends to just wander around chasing enemy armies.
All things being equal you will get the highest contribution to the Crusade and your beneficiary will become King of Jerusalem. Wait for the message box that asks if you want to now play as them and choose “I wonder what kind of King he will be…” and boom, you are now the only independent landed Karling!