The solder hardens even before I can bring the PCB adapter near the LCD and I am unable to get them to stick together.
Any advice would be appreciated - I'm also finding it difficult to cleanly attach the pins on the shield to the Arduino board, but I suspect this is just a matter of straightening a few pins.
So you applied solder to the corresponding pins (one on each) on the adapter and the board, then placed them next to each other - and reflowed the solder to join them? It looks like it would take patience, but it should be possible. You might try "clamping" the two boards together (positioned properly) with an alligator clip - then soldering one or two of the pins together - then remove the clip and continue with the remaining pins...
You should plug the pins into the Arduino connectors and assemble the shield to the pins before soldering them. That will ensure that they are properly aligned.
I'm not sure that's the part with the issue - I think the OP was referring to the small PCB adapter piece shown in the photos in that link...? Maybe we need more information...
Not impossible, the picture clearly shows well soldered joints...
I think the person attempting to do the soldering needs some soldering experience or someone who has that experience to do it for him, there is nothing in the picture that looks at all difficult. From the description he gave of his less than successful attempts it sounds like he is not heating both surfaces equally hot enough to melt the solder. Heat both the pad and the pin equally hot enough to melt the solder (place them together first) put the solder on the work, not the iron, you can touch the iron with the solder a little, just enough to start to melt the solder but you must heat both pieces equally, apply the solder and NOT MOVE them until the solder cools or you will have a bad solder joint, just a couple of seconds is all it takes.
The Adafruit module looks easier to use... 1.8" display and 10 jumper wires and load the demo's and libraries restart the ide and compile and run the samples also has an SD card slot that can be read using the same interface as the TFT, for a Tiny display mine looks pretty good... Easy to use the samples to really use the display with your own sketches too...