How to use solderless breadboard

I have a solderless breadboard that I am unable to connect to:
robotshop.com/ca/productinfo.aspx?pc=RB-Spa-290&lang=en-US

How do I accomplish creating a solid connection between this component and a solderless breadboard without solder?

I have already drilled out solder and plastic from numerous failed attempts with this chip. Soldering is not an option anymore.

Soldering pin headers is really the only option - that was the purpose of the breakout board for that chip. You would solder standard headers to the pins (straight or 90 degree) and that would allow you to easily connect it to a solderless breadboard. If you can upload an image of the current state the module is in, perhaps we can think of other options so it can be salvaged.