My only tip is to build a box on a platform saddle quetz with one side open and a gateframe on that side, and trap the Phoenix in there with a gate once it is in. I then use a flamethrower to take it. Hope this helps.
You can get it to spawn next to your base because of the following: It always respawns at it's last location, so if the heatwave ends while you are following it you will know where it is for the next heatwave. It also chases you when you eat flowers... hint hint
Find a phenix during a heatwave and follow it until it ends. The phenix will turn into ashes and land on the ground but will spawn right back at the same exact spot during the next heatwave. Build a trap 6 blocks high so I can't glitch out and you have yourself a trapped phenix to tame:)
This Might Take you a day or so but how I got my pheonix was i would look everywhere for a pheonix during a heatwave and you have to wait for the next heatwave to start this when you see the pheonix follow it and when it goes to the ground build a trap above where it despawned and when another heatwave starts it will be trapped: REQUIRED JERBOA AND FIRE WYVERN
Fun fact! You can tame the Phoenix by hitting it with a torch so you don’t have to waste you’re time shooting it and missing and what not just wanted to help everyone out because this creature is definitely something worth getting