The Legendary Gun is probably the easiest to get as you can start looking for it as early as level 1. In order to get it you must first obtain the Rusty Old Gun as that will enable you to encounter the Ancient Anvil machine room through ? rooms (or the gear icon if you have the artifact that reveals those rooms.



Once you have the Rusty Old Gun and find an Ancient Anvil machine room you can then spend crystals to convert it to the Restored Gun. You'll then have to find that room a second time in order to turn it into the Legendary Gun.



The first conversions costs 200 crystals to "Restore an Old Gun" and the second one costs 450 crystals to "Reforge a Restored Gun" and gives you the Legendary Gun. The achievement will only unlock once you pick up the gun so don't forget to do so before leaving the room!

The Gold Froggy is likely the second gun you'll get here as it takes a bit more work to acquire. In order to obtain it you must first pick up all 3 of the colored Froggy guns - blue, red, and green.



After doing so you can start checking the ? rooms for a golden frog statue machine room:



Once you find this room you simply interact with each pedestal which will then grant you the Gold Froggy and the achievement. Again, don't forget to pick it up before leaving!

NOTE: this achievement is currently bugged and cannot be completed

The Incisor is undoubtedly the last of the "secret" guns you'll unlock as you first have to make your way to level 8 and beat the boss there to collect the final android orb. Once you have that and give it to Maria (the lady in the starting area above the portal to start the game) it will unlock the Tinkmater's Goggles:



Then, you "simply" have to find this in-game when it's unlocked and hope that it changes a weapon into the Incisor and not the Tailgun.