It looks like you can't do what I suggested with just one DAP-1522.
So you have three things you can do I guess.
1 -
You can get a rangebooster and broadcast at G <= not a bad idea, you would only likely notice the N speeds when you are doing internal transfers of data inside your complex anyways, unless you're lucky enough to have a ISP giving you fibre.
2 -
Buy a DAP-1522 or 1555, set the switch to AP mode, run an ethernet cable to it from your router <= involves running an ethernet cable to where you want the AP (second floor) and you shouldn't be using more than 300 feet of ethernet cable, so you may be restricted to where you can put the AP
3 -
Buy two DAP-1522s or 1555, set first one to Bridge mode, connect to the router network wirelessly, connect the second DAP to the first using a short ethernet cable, set the second one to AP mode, setup the wireless <= Expensive, and Quality of the Bridge mode may not be very good or reliable
Note that the APs need to be placed by an outlet

And having them out in the hall is generally better than in a room.
Same with the router, while it has it's security flaws, you're going to get better reception in the building if you get the wireless into the halls.
When I was setting up for college dorms, we would place a bridge in the attic of each dorm, bridge an area of dorms together, (we were using outdoor quality dedicated bridges), we would run a connection to a services room in each dorm, and in that room we would place a switch. We ran cable from the switch to each floor and attached an AP on each floor, at opposite ends. So the first floor might have one 25% down the hall, the second one would be 75%, third would be 25% again.
We were wall mounting the APs about 2-3 feet from the ceiling.
Even with this setup, we had a hard time. These APs and router's would cut out all the time, they aren't made for 50 devices to be connected to each one 24/7. And turn out to be real flaky.
Hopefully you find a way to make this work for your apartment complex.