The Bullet Train achievement in Hitman 3 requires you to take out a guard with a silenced pistol, a shotgun, and an SMG. This is an easy achievement to unlock and can be completed during the game's final mission, Untouchable. You’ll need to kill three different guards with all three weapons to get the achievement to unlock.
Throughout the mission, you’ll be taking out guards armed with pistols. Make sure you pick one of these up. About halfway through the level in one of the train cars, you’ll come across a workbench. Here you can craft a silenced pistol. Once crafted, carry on making your way through the train and make sure you kill at least one guard with it.
As for the SMG and shotgun, you might be able to pick either one up off a dead guard as you work your way through the level. If not there is an armoury train cart shortly after the workbench area that has both a shotgun and an SMG on a table. Pick those up and kill a guard each with one of those and the achievement should unlock.
(Thanks to Elite1111111111
for pointing out my error!)