For all the weapon achievements, you do not need any points invested into it's respective skill. The only thing that matters for these achievements is that your aim is right, and that you do exactly what you need to for each respective weapon. You don't even need to kill your enemies to fulfill the requirements for each achievement.
In order to score critical hits with the pistol, whenever you have the aiming reticule on an enemy, it will slowly being to change from yellow to red. During this time, your crosshair's will begin to tighten up, allowing one precision shot. Make sure that you are zoomed in, which you can do by holding . Moving in any way will reset this entire process, so try not to if possible. Hitting anyone after your crosshairs are completely red will automatically deliver a critical hit. Having the Chain Shot skill from the Pistol tree is an automatic critical hit for every shot, so use it often.
Also, if you die, any progress you have made towards these achievements will be lost. Your progress will not carry over, so be careful! Any progress towards this achievement will also not carry over into other playthroughs, so you need to get all the hits before you finish the game.
You will unlock the perk "Pistol Proficiency" after scoring fifty critical hits with the pistol.