Like Snarky said the Rebirth Destiny incarnate will let you pick up the healing badges so you don't really need any particular archetype to collect all the badges. (Joining MSRs and spamming Rebirth got me the first three heal badges in just a couple of months. It can certainly be done faster if you're really active.) That said, obviously having healing powers as you level up makes for a nice head start on getting the badges,
Aside from that, stealth and flight will help you get exploration badges more easily. Stealth also lets you speed through a number of badge missions. If you don't want to spend a pool pick on flight, just grab a jetpack from P2W or by Firebase Zulu. Good AoE damage is very helpful when it comes to the various defeat X badges though, again, the Judgement Incarnate lets any AT have a strong AoE attack.