Begin Edit: I have an easy, working solution for this, and for the similar achievement for 200 tags. That solution is posted on the other achievement, so I refer you there.
Hopefully someone can offer guidance. Is it okay for me to reference another solution? Or should I essentially double post that solution here? :End Edit
For clarity, this means you must have 100 unspent tags on your counter. Those tags used for upgrades will subtract from this total, so spend them wisely or not at all.
In a run through all seven areas, I collected 236 tags. You definitely could afford some upgrades if you progress through most of the game.
Note that you can pick up items while rolling. Use this to safely grab tags covered by enemies if you can't get to them otherwise.