You will first run into Trace in the back of Ninn's Boutique on Disc One. He creates rings that have multiple effects by combining rings. As the story progresses, you will he will appear at various locations and eventually have more rings that he can make.
When at the menu, you will notice that the yellow highlighted rings are the ones you have the necessary materials to make (the game does not count rings you currently have equipped).
Level 1 Rings[]
Name Type Rings Ring Components Fire-Powered Ring Fire Lv 1
Damage Up Lv 11 x Flame Ring
1 x Bruiser Ring3 x Magma Fragment
4 x WhetstoneWater-Powered Ring Water Lv 1
Damage Up Lv 11 x Aqua Ring
1 x Bruiser Ring3 x Cold Water Stone
4 x WhetstoneWind-Powered Ring Wind Lv 1
Damage Up Lv 11 x Wind Ring
1 x Bruiser Ring3 x Wind Seal Leaf
4 x WhetstoneEarth-Powered Ring Earth Lv 1
Damage Up Lv 11 x Earth Ring
1 x Bruiser Ring3 x Quality Iron Sand
4 x WhetstoneSoul Ring MP Absorb Lv 1
Damage Up Lv 11 x Osmosis Ring
1 x Bruiser Ring3 x Magic-Luring Stone
4 x WhetstoneTurtle Shell Ring Hardened Killer Lv 1
Bio Killer Lv 11 x Piercing Ring
1 x Bio Ring7 x Hard Skin, 2 x Whetstone
6 x Insect Innards, 2 x WhetstoneFlying Beast Ring Beast Killer Lv 1
Aerial Killer Lv 11 x Beast Ring
1 x Aim Ring4 x Beast's Horn, 2 x Whetstone
3 x Sharp Beak, 2 x WhetstoneHerculean Ring Damage Up Lv 1
Critical Up Lv 11 x Bruiser Ring
1 x Anger Ring4 x Whetstone
4 x Sticky Tape
Level 2 Rings[]
Level 2 Rings are available after you create a Crusher Ring.
Level 3 Rings[]
Level 3 Rings are available after you create a Demolition Ring.