Unable to burn bootloader of Pro Mini 3.3V 8MHz using Arduino as ISP

I've struggling for the past few days trying to burn bootloader of Pro Mini 3.3V 8MHz using Arduino as ISP. Before getting into the question, I would like to make sure my understanding of Pro Mini is correct. I'm trying to program Pro Mini and in order to do that I have to burn bootloader of Pro Mini or else I will face error like stk500_recv() programmer is not responding. Do correct me if I'm wrong.

So back to the question, I keep facing error like Reading | ################################################## | 100% 0.02s

avrdude: Device signature = 0x000000 (retrying)

Reading | ################################################## | 100% 0.02s

avrdude: Device signature = 0x000000 (retrying)

Error while burning bootloader.
Reading | ################################################## | 100% 0.02s

avrdude: Device signature = 0x000000
avrdude: Yikes! Invalid device signature.
Double check connections and try again, or use -F to override
this check.
when I try to burn the bootloader of Pro Mini.

OR this error
Error while burning bootloader.
Reading | ################################################## | 100% 0.02s

avrdude: Device signature = 0x00ff00
avrdude: Expected signature for ATmega328P is 1E 95 0F
Double check chip, or use -F to override this check.

PLEASEEE help me solve this. I'm a total newbie, sorry if I did any silly mistake. Do let me know if the error shown above is not complete enough.

It is HW problem. You are trying to upload 3V3 target with 5V source. Wrong! It can destroy the target. Use 5V power for the Mini during the upload. It is 5V tolerant so no worries. However, if the Vcc = 3.3V, pin level form the UNO exceeds Vcc and can cause damage of MCU.

Data wires seems to be connected correctly.