I usually hear "bring out the big guns" instead of 'bust out the big guns,' but the meaning is the same:
This is a time to get more serious, use more tools, get more help, etc.
Me: "This is too heavy, I cannot lift it."
You: "Okay, this is a time to bring out the big guns. We can ask some friends to help."
Me: "I have a very, very, very hard English question for you."
You: "Okay, time to break out the big guns. Let me get my dictionary and schoolbook and workbook and I will try to answer your question."
Me: "I can do this job"
You: "No, it is too hard for you. I am going to get a better worker to do it."
Me: "Oh, time to break out the big guns, hmmm?"