Problem with ESP8266, wrong voltage?
The ESP8266 has a relatively high peak current requirement compared to general microcontrollers. This is rarely fully understood. There is a lot of information on the Internet that says the current requirements is about 70mA. But that is a long term operational average. The peak current requirements can be as high as 1/2 an Amp. 

When the ESP8266 starts one of the first things it does is an analog calibration. This is where it draws more current. If the power supply can not maintain the minimum required voltage at that current the voltage dip will cause a failure. The duration of this dip can be very short. A digital scope needed to see the fault. 

I tend to recommend the use of ESP8266 modules that have an onboard regulator. Modules like the Wemos and Nodemcu type boards. 

Using modules like the ESP-01 or the ESP-12 type modules (no regulators) are a lot more touchy. What you need to do is keep the 3.3v regulator as close as possible to those modules, and short solid connections. It also helps to have some additional capacitance across the 3.3v connections at the module.

Breadboards are convenient to use but they also can be the source of poor connections. 

Consider what I have wrote here, how it applies to your setup. You may also want to solder an additional capacitor on the module. Vcc to ground. Something like 200-470uF, right onto the top of the module.