The Black Ops 3 Spire map is set in a space tower that a futuristic society built to speed up transport around earth. This looks like an airport, but it is way up in the sky. With this in mind there is one exterior wall run location that you will need to use. You can run into the main lobby or you can jump to a loading zone and head directly to the other side of the map.
Dropping into the center lobby is dangerous because there are overlooks on each side, funnels into each side and a center door that allows enemies to appear on either side of a small wall. In short, if you drop into this area you need a plan to get to one of the corners or you will die fast.
If you can set up shop in the upper rooms you have a good chance of locking down that lobby. This works best with a two man team, with one player checking the door to the center room and watching the back.
Using a launcher on this map is very helpful, and if you can earn a Hardened Sentry on your streaks you will be able to deploy it on either of the overlooks to lock down the center.
If you stick to the hallways and avoid the lobby you can find success with the shotgun, but otherwise I recommend a SMG with decent range so that you can win firefights in many areas. Thanks to the two overlooks and the plants below that offer a hiding spot you can find some success with a sniper if you are quick.
The video above offers a walk-through of Spire in the Eclipse Black Ops 3 maps. There are places to wallrun, including on the interior walls, so give it a look to see where you should focus your attention the next time you play.