Challenges - universal across characters?

I started the game yesterday as a warrior, got up to mid 20s in level, and started a wizard, at which point I found you can drag your other characters along for the ride and they level up and get equipment etc along with you. Are the challenge achievements that give bonuses universal? I.e. I like controlling the wizard and letting the warrior go auto. If I decide to change that up, are my challenge achievements carried over or does each character have their own sets of bonuses depending on who you control?