The strategy for this will be pretty much the same as for getting 5 skulls on every level. The main problem you'll encounter is that essentially all preparation time has been taken away. You will get three seconds at the beginning and three seconds in between every wave to prepare, and that is it.
To deal with this, the best thing to do is to look around the level and re-familiarize yourself with it (assuming you've already mastered it on War Mage, getting 5 skulls). After doing this, choose your loadout accordingly and do your best to recreate your winning strategy. Just remember you may have to re-prioritize and adjust your strategy to do things quicker. Make excessive use of the sprint button (clicking the left stick) and set things up quickly, not neatly. If things are not perfectly symmetrical or the exact same at either side of the map, you don't have time to fix it. You should also try to not spread your traps out too much, and keep them closer to you. Set up essential things, like barricades, in the beginning when the waves will be easier to manage by yourself. Try using the portals a lot, too.
To counteract the loss of preparation time, since it is no longer required for you to get 5 skulls, enjoy the freedom of letting enemies into the rift or even dying and not having to start over.
Two other things about Nightmare mode should be noted. You will still get the large coin bonuses every three or four waves and your guardians (Archers and paladins) will not respawn at these times as they usually do, and dead guardians still count towards the total amount of guardians allowed, so do not rely to heavily on them for support.
For other more general play tips, see the guide for "Ultimate War Mage". If you are having trouble with a certain level, check the guides at xblafans.com or check YouTube for countless other videos. There's also a useful thread here that covers most of the levels.