Rare Replay

There are 15 weapons to find and use, most of them you'll find just playing the first half of the game. To get them all you will need a yellow key and the SpaceStation and Water Ruins levels.

The yellow key can be found at:
Juno: Goldwood, Outset (hidden in a box in the caves)
Vela: Cerulean, Dune (holding room)
Lupus: Spawn Ship, Troop Carrier (sewer pipe)

To open the levels:

Full Weapon list:
Pistol
Machine Gun
Shotgun
Homing Missiles
Tri Rockets
Sniper rifle
Flamethrower
Shocker
Grenades
Shurikens
Remote Mines
Timed Mines
Cluster Bombs
Flares
Fish Food

Having played through the first part of the game and gaining the Jetpacks I only needed the following weapons:

Remote Mines (Tawfet):
Head through the level to the area you re-build Floyd in.
Go into the tunnels underneath via the chimney and inside will be some conreate blocks, blow this up to find the secret tunnel.

Timed Mines (Water Ruins):
When the level loads head to the big island in the middle, circle around the outside of it towards the right for this chest.

Shocker (SpawnShip):
As Vela Take the elevator at the start and head through the door. Drop down and enter the underwater door. Continue through these rooms to find the Shocker.

Shurikens (Goldwood):
Head through the Yellow key door near the water at the start, it's to the left as you look at the hut.

Flamethrower (SpaceStation):
Go to the Spacestation and hop down enter the room on the side and use the crates to jump up two floors. Turn around and you'll see the chest in front of you.

If you have trouble locating any of the weapons, leave a comment and I'll try to help you out.