Emphasis mine.
You need to meet the prerequisite when you are taking the feat, not at the end of the levelling up process. That's why they're called prerequisites, and not postrequisites.
In the case of Battle Caster, if you haven't don't already have "the ability to ignore arcane spell failure chance from armour" (its prerequisite) before you take the feat, you cannot take the feat.
Besides which, I don't believe the list of things to change on pages 58 and 59 are an order of processes, merely a list of things to alter as you level up.
