• Only kill your targets:

First of all, you must not kill anyone that is not a target. Watch out for bullet penetration when the target has people around them, on the other hand, killing several targets with a single shot is OK.

Remember, you can change disguises and knock people unconscious, just make sure not to be spotted while doing so, as you cannot kill an unconscious witness who is not a target.

• All targets must be killed with a sniper rifle:

This condition requires you to shoot the targets themselves with the sniper rifle, as Shooting something to cause an accident, or in the case of Sapienza; shooting the telescope, will not count as sniper kills.

Keep in mind that targets like destroying the virus in Sapienza, does not require to be done using a sniper rifle, just make sure not to kill anyone else while doing so.

• Do not get Spotted:

It helps to point out, that the bodies of the targets can be found, you won't get Silent Assassin rank, however this is not a requisite for the Sniper Assassin challenge, and this guide is for the basics, you are more than welcome to challenge yourself to a Silent Sniper Assassin suit only run.

Something to consider, is that if you fire your sniper several times from the same spot, enemies may start shoot in your general direction, and head to the area you are shooting from, this however doesn't mean you have being spotted, whoever depending on the location, you may find yourself unable to leave your sniping position as the way out is trough all the searching enemies that have gatherer around.
Proven false after further testing, if the targets go into lockdown, the guards seem to know your location and see trough your disguise.

• Finish the mission:

Finally, you are required to escape. This can be done so by any means that are available to you, but remember to stay undetected, less the run is forfeit at the last moment.

While it is possible to get Silent assassin while delivering the killing blow with a sniper rifle, which would give you both challenges. Getting the Silent assassin mission rank is not required for the Sniper assassin challenge. Most direct methods of getting Sniper assassin will have the bodies being found eventually, which does not negate the Sniper assassin challenge, as you only need to not be spotted yourself. You are free and encouraged to challenge yourself to do a Silent sniper assassin run, just remember, if you are only looking to unlock the Sniper assassin challenge, the bodies being found is not a fail state for the challenge.