DivineAngel

First off, some of the treasure, and particular the smaller ones, can be found in more than place. Since you only need to discover one of each I will give example locations for them rather than sit here all night detailing all the places.

Gold Ring-Defeat the executioner Majini in Public assembly. Also, Defeat Uroboros without using the furnace.

Ivory Relief-Defeat the blonde headed Cephelo in the Urban district

Heart of Africa-Defeat Wesker before the seven minutes are up and the heart of Africa will be revealed between the two stairs on the ground floor at the start of the battle with Jill.

Soul Gem-Defeat Popokarimu in the caves instead of fleeing up the stairs.

Power Gem-Left behind by defeated Reapers.

Lion Heart-Certain Licker Beta`s will drop these.

Blue Enigma-Dropped by Giant Majini in the marshlands and caves/pyramid.

Gold Beetle-Inside the pyramid (after Caves). On the third puzzle floor you must open the optional doors to find it.

Diamond Marquise-As Chris, before getting to the bridge that collapses in the last battle with Wesker, shoot at the side of the rock to your
Left to create a bridge that will lead you to the treasure.

Diamond (Brilliant)-Inside the mine, just before you get to the crank
That opens the gate to the area where lots of majini attack you, look around for an easy to miss path (it has a couple of skulls on it)that will lead you to the trunk that contains the treasure.

Royal Necklace-In the control room (chapter 5-3) just before you exit the area.

Dead Man`s Necklace-There is two to be picked up right next to the "failed" experiments on the conveyor belt in chapter 5-2 also, after defeating the Gatling gun majini for the first time, you will come to a room where you need to hide behind crates from rocket-launcher weilding majinis. These three also drop the treasure.

Sapphire/Emerald Oval-You must nab these BEFORE the battle with Wesker ends. The former can be found inside a vase near the area where you collect the L.Hawk and the latter inside the sarcophagus where you collect the L. Hawk (upstairs).

Emerald (Brilliant)-You must nab this BEFORE the battle with Jill ends. Can be found at the far end of the east balcony.

Venom Fang-Dropped by the two chainsaw majinis in the oil refinary.

Antique Clock-Chapter 1-2 in the building that has two locked doors but one open door underneath the stairs to the upper locked door, right near the corner. You can enter from there.

There is loads more treasure to be found but I`m not going through them all. The strategy guide tells where you can find all treasure types though only gives one example of each since some can be found in more than one place.