I've had good luck with Amdro. Giant mounds don’t sound like fire ants. We have lots of those big mounds here, though I’m not sure what type of ant they are. Big and black is all I know.
I have big ant mounds to. They usually are quite soft. I can't imagine anything closer to being nuked than when I raise my Woods rotary cutter up over them and lower it. There just ain't nothin' left. Never had one rebuild after nuking.
In the past I have used the ant killer products available at retail stores. This year I tried spraying Permethrin around a few red ant mounts that had popped up. They were gone within a day or two.
A few years ago I started buying Permethrin from the local farm supply in 10% concentrated form. Initially I used it for tick control on the 4 acres where we are building our house. It did a great job of controlling the ticks at a cost of around $10 an acre.
So far mine have not come back. I have sprayed a large area around the mounds. At the build site I spray a couple of acres. I have not had an ant problem in that area at all.