Follow during heat wave. Using a pillar you can locate precise location of its position on the ground. Use rare flowers if you want To agro this beast. Make it follow you to a prime location if possible (very unpredictable). Build a 3x3 square trap 6 high, above it's location and enclose with ceilings. (Stone preferred) Use any method to tame but it requires some serious flames to tame. If you don't get it the first time repeat your trap ontop of your current build now your 12 high with another ceiling ontop. So on and so on until it's tamed. It will leave your trap if you leave render distance(beware) when it spawns you better be there at the trap.
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:)
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
It introduced a new taming method,while not the pseudo-boss we prayed 4 but to tame it u set it on fire with flame arrow,flame throweror a fire Wyvern,they only spawn during heat waves.keep this in mind.