How to wirelessly bridge two routers?

I’ve been scouring the web, watching YouTube tutorials, and digging through forums, but I’m hitting a wall—it feels like this is a universal headache, and honestly, I'm probably just not tech-savvy enough to find the answer myself.
So, I signed up for a triple-play bundle and they gave me their provided router—a Netgear Nighthawk. It doesn't have any external Wi-Fi antennas. It's sitting downstairs on the ground floor, hardwired, obviously. I can catch a signal upstairs, but it's incredibly weak and keeps dropping out on me. Before we switched to this service, we were using some old connection through a TP-Link router. I still have that same router lying around, and I was wondering if it’s possible to wirelessly bridge the Netgear Nighthawk with the TP-Link—basically, have the TP-Link pick up the signal from the Netgear and then broadcast it upstairs so I can connect to it wirelessly. Is that even doable, and if so, how?

P.S. The Netgear only has four yellow LAN ports. The TP-Link has those four yellow ones plus one blue WAN port.

P.P.S. TP-LINK TL-WR941ND

That Cisco unit has internal antennas... which honestly isn't nearly as good as having actual external ones sticking out of the case.

If you're already dealing with a weak signal upstairs, even that TP-Link router won't be able to pick up much from the Cisco device, so the core issue stays the same.
You might get a stronger connection if you switch over to "b" mode, but you'll take a massive hit on speed—we're talking maybe 20Mbps—assuming your neighbors aren't all hogging the bandwidth on the same frequency.

Your best bet would be to just run an Ethernet cable from the Cisco unit up to the next floor and plug that TP-Link straight in.

Another way to play it is to connect the TP-Link to the Cisco unit downstairs using a short 1-2 meter patch cable. Since that thing has better antennas and higher power settings, it might actually push a usable signal upstairs. Try laying those stick antennas flat horizontally; they tend to radiate upward better that way.

There are probably other ways to hack this together, but I don't feel like digging through a manual right now.....

ps: check to see how crowded your local airwaves are. If there's a lot of interference, try setting a fixed channel where the signal is weakest.
Then you can just kill the Wi-Fi on the Cisco and set up your SSID and password on the TP-Link instead.