Buster (Destroy 1000 objects) - just before doing the airfield mission you move forward with a man from the resistance. At one point there is an area with unlimited panzer rockets that respawn you can use these to destroy nearby objects and just change zones and go back to respawn all objects.
Rampage (Kill 200 enemies with Empower) - same place, just use empower and shoot enemies with the panzer, change zones and go back to respawn them.
Honorary Geist (Spend two hours in the Veil in single player) - leave your Veil sight on and stand in a Veil portal thing, then just leave it for 2 hours.
Time Out (Use the Mire power for more than an hour in a single player) - Stand in a Veil portal and turn on Mire, when your Veil power runs out, let it fill up and repeat (you can tell when your Veil power has run out using Mire because your controller will stop vibrating, this allows you to do something else while you keep turning the Mire power on).