I suspect that the DTR pin is not hooked up. Even if you are going to reset manually without a 0.1uF capacitor, you need to hook that one to your RESET or RST of the Arduino.
If you do not use the "Auto-Reset" cap, you are going to have to wait till the "Uploading..." appears in the monitor and press the reset on the Mini then watch the USB2TTL's Tx LED for two quick blinks, then release the reset button of the Mini. If it goes three, it will be too late.
I apologize. I just disconnected the DTR on one of my projects and it did load, but only with a reset button.
I am looking, but I can not find a reset button on your Arduino. You could bridge pin 22 and 23 on the Mini and that should reset it.
Other than that, you are going to need a 0.1uF cap in series from the USB2TTL pin 4 (on the right hand side and without a header pin) to pin 22 (above the 5v Vcc). I suppose you could get a piece of wire into the hole to connect the pad and plug the other end into the breadboard. Then, see if a 0.1uF leads will span the distance.
Either way, you have got to catch the bootloader in the middle of booting or the sketch will not load.
I am not sure if the Mini is bootloaded. What does that mean (I am new to this). Also what does the 0.1uF capacitor in series from the USB2TTL pin 4 to pin 22 do? I will put in the capacitor tonight when I get home from work. Thanks for all of the help.
Bootloader are a setup program that allows sketches to be loaded through the serial UART on the ATMEGA. A loose concept is the bootloader being the operating system and the sketches as files that you can only can load one at a time. If your mini has an LED hooked up to D13 of the Arduino, you should see a it blink rapidly 4-5 times when you plug it in.
The cap just allows you upload without having to manually reset the Arduino. The Data Terminal Read or DTR will send a signal to the reset pin when it is ready for uploading. The bootloader will then direct the sketch to the appropriate section of flash memory, reset and start the sketch running. Without all this, you just get the error you stated in the OP.