Please note that your question is stated incorrectly - you don't provoke an attack of opportunity for moving INTO a threatened square, but for moving OUT of one. From Attacks of Opportunity, emphasis mine:
Moving out of a threatened square usually provokes attacks of opportunity from threatening opponents.
Having said that, when using Acrobatics to try to avoid provoking, the doubling is done on a square by square basis.
To re-quote the Acrobatics skill:
In addition, you can move through a threatened square without provoking an attack of opportunity from an enemy by using Acrobatics.
The FAQ clarifies this:
Acrobatics allows you to make checks to move through the threatened area of foes without provoking attacks of opportunity. You must make a check the moment you attempt to leave a square threatened by an enemy, but only once per foe. The DC (which is based of the Combat Maneuver Defense of each foe), increases by +2 for each foe after the first in one round. The DC also increases by +5 if you attempt to move through a foe. In the case of moving out of the threatened square of two foes at the same time, the moving character decides which check to make first.
For example, a rogue is flanked by a meek goblin and a terrifying antipaladin. The rogue move away from both of them, provoking an attack of opportunity from both, but uses Acrobatics to attempt to negate them. She must move at half speed while threatened by these foes and can choose which to check against first. If she fails a check, she provokes an attack of opportunity from that foe. If she makes it, she does not provoke from moving through that foe's threatened space this turn.
So you are moving at half speed whenever you are in anyone's threatened area and using Acrobatics to avoid AoOs. Yes, you have to spend 2 feet for every 1 feet you wish to move (in increments of 5' squares). Or more (if you are already in difficult terrain, for example, your move is already 2:1).