This achievement is pretty straight forward, and you can probably pick it up without even trying as most of the weapons appear in later levels. There are a total of 16 weapons you must pick up, and kill someone with. The list below contains the weapon, the level, and wherein the level they are approximately first located. This may contain spoilers.
MP7 - Dropped off guards.
MP5 - Dropped off guards, and found behind truck after jumping out of the office.
Grenade Launcher - Found in catacombs.
12 Guage - Found on 3rd of 4th guard after car chase.
AK74 - Same area as 12 Guage.
G36 - Found in the last room toward the end of the level. I found only a couple guards had it here.
M3T - Found off guards in refinery while turning the valves.
DSR-1 - Found next to intel, and toward the end of the refinery before Nicole picks you up.
UMP - Found on guards on Hovercraft.
PCP-1000 - Stun gun. Found off first cop you takeout, after the truck chase.
M9 - Found on first guard after you escape your cell. This seems to be the only place this gun is located. Kill the guard in the next room with it to get credit.
M1 - Found on guards shortly after you leave cell area.
Combat A.R. - Found shortly after the M1.
M24 - Found next to intel around the area you hit the switch to lower a lift, toward the end of the level.
The P99 and Silenced P99 are Bond's default weapons, and you will start the levels with either, so make sure you get at least one kill with each.
This accounts for all 16 weapons, and again they appear various times again with exception to the M9 and the stun gun. You should be able to get this achievement no problem.
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