There are 12 available weapons and 1 hidden weapon for 13 total. You can buy these at the 3D printer that unlocks at each antenna site once you power it up.
You only need 12 to unlock this achievement. The weapons are:
Blaster of Disaster - $450
The Obliteratorrrr - $2300
Nut Hugger - $2300
Lazer Blazer - $450
Tazer Spazer Annihilazer - $2300
Morphinator - $2300
Punches in Bunches - $450
Nerve Reaper - $2300
Grape Popper - $2300
Iron Fister - $450
Bulldozer - $2300
Hellfire - $2300
You get "money" called Hemoleum from multiples sources:
Glowing green barrels like from the beginning of the game (Random small amounts)
Looting dead crabs (Random small amounts)
Queens (Random amounts usually $300-$500)
Clutch Nixon missions ($1000 each mission)
And finally once you have powered all the antennas and have extra power cores (which you will have after killing all the Queens for The Queen is Dead! achievement) you can exchange them for Hemoleum at a rate of 1 power core = $1000.
At the end of the game if you kill and loot all the Queens and do all the Clutch Nixon achievements you will have enough to buy all 13 weapons and all upgrades and equipment with no issues after exchanging your excess power cores.
If for some reason you don't you will need to grind by killing and looting crabs or by finding green barrels.