There actually is a Flayer Spear, You get it by getting 5000 points in the Roller coaster game in the speed square on disk 2 and 3... Anyway Here it goes...
Gatling Gun Initial Equip

Assault Gun : Defeat Guard Scorpion

Atomic Scissors : Steal from Custom Sweeper

Cannon Ball :Kalm Town

W Machine Gun : Mt. Corel Railroad

Heavy Vulcan :Cosmo Canyon

Enemy Launcher :Nibelheim

Drill Arm :Cid's House

Chainsaw :Wutai

Rocketpunch :Temple of the Ancients

Microlaser :Icicle Inn

AM Cannon :Mideel

Solid Bazooka :Costa del Sol

Max Ray :Sector 8

Missing Score :Sister Ray, before Hojo

Wow that took awile... I think I got them all... If I missed any correct me

Q: How do you obtain Cid's Mop?