How to transmit UART from STM32 to PC without TTL to USB converter?
There are a few options to communicate with a PC using serial, but not necessarily over UART.


There is a minimal chance that your PC has an RS-232 serial port. But as it is an RS-232 port you cannot connect the MCU's UART directly. You will have to use a MAX232 chip for example.
Now, ut would probably be easier to get a TTL-to-USB converter then building one converter for RS-232.
The third option would be to go with USB on the MCU at the first place as @DiBosco suggested already. Using the STM32F429 Discovery board the required hardware is already at hand, the micro USB connector can be used for custom USB applications.

To setup the USB on the STM32 using STM32CubeMX you can follow this detailed description from Stack Overflow.

Once it is done, your MCU will enumerate as a virtual COM port on your PC when plugged in.