This achievement can be done in single or multiplayer and can be done over many different missions (i.e., not in one mission). Make sure you buy the original handgun you are given. Picking up a gun does not count. You only need to buy the attachment for one gun, not for every gun.
What you need to get:
HANDGUNS:
Five Seven,
USP 45,
MP412,
Desert Eagle,
.44 Magnum,
P99
MACHINE PISTOLS:
G18,
Skorpion,
MP9,
FM99
ASSAULT RIFLES:
M4A1,
M16A4,
SCAR-l,
ACR 6.8,
AK47,
FAD,
G36C,
CM901,
MK14,
Type95
SUB MACHINE GUNS:
MP5,
UMP5,
MP7,
PM-9,
PM90M1,
P90
LMGs:
M60E4,
PKP Pecheneg,
MK46,
L86LSW,
MG36
SNIPERS:
MSR,
Dragunov,
RSASS,
L118A,
AS50,
Barrett .50 Cal
SHOTGUNS:
Model 1887,
USAS,
SPAS12,
KSG12,
AA-12,
Striker
ATTACHMENTS:
Holographic Sight,
Red Dot Sight,
ACOG Scope,
M203 Grenade Launcher (e.g. M4A1),
M320 Grenade Launcher (e.g. ACR),
GP25 Grenade Launcher (e.g. AK47),
Grip,
Shotgun