The rivalry trophies are obtained through a rivalry game. You have to win the game but you can win it in any game mode, even free play.

Trophy	How to Unlock
Administaff Bayou Bucket	Houston Vs. Rice
Apple Cup	Washington Vs. Washington State
Beehive Boot	BYU Vs. Utah, Utah Vs. Utah State, Utah Vs. Weber, Utah State Vs. BYU, BYU Vs. Weber, or Utah State Vs. Weber
Black Diamond Trophy	Virginia Tech Vs. West Virginia
Bronze Boot	CSU Vs. Wyoming
Commander-In-Chief's Trophy	Air Force Vs. Army, Army Vs. Navy, or Air Force Vs. Navy
Commonwealth Cup	Virginia Vs. Virginia Tech
Cy-Hawk Trophy	Iowa Vs. Iowa State
Floyd of Rosedale	Iowa Vs. Minnesota
Fremont Cannon	Nevada Vs. UNLV
Golden Boot	LSU Vs. Arkansas
Golden Egg Trophy	Mississippi State Vs. Ole Miss
Golden Hat	Oklahoma Vs. Texas
Governor's Cup	Kansas Vs. Kansas State
Governor's Cup	Kentucky Vs. Louisville
Governor's Victory Bell	Minnesota Vs. Penn State
Illibuck	Illinois Vs. Ohio State
Ireland Trophy	Boston College Vs. Notre Dame
Iron Skillet	SMU Vs. TCU
Jeweled Shillelagh	Notre Dame Vs. USC
Keg of Nails	Cincinnati Vs. Louisville
Land Grant Trophy	Michigan State Vs. Penn State
Little Brown Jug	Michigan Vs. Minnesota
Maloof Trophy	New Mexico Vs. New Mexico State
Marching Drum	Kansas Vs. Missouri
Megaphone	Michigan State Vs. Notre Dame
Missouri-Nebraska Bell	Missouri Vs. Nebraska
ODK - Foy Sportsmanship Trophy	Alabama Vs. Auburn
Old Brass Spittoon	Indiana Vs. Michigan State
Old Oaken Bucket	Indiana Vs. Purdue
Paul Bunyan Trophy	Michigan Vs. Michigan State
Paul Bunyan's Axe	Minnesota Vs. Wisconsin
Peace Pipe	Bowling Green Vs. Toledo
Purdue Cannon	Illinois Vs. Purdue
Seminole War Canoe	Florida Vs. Miami
Shillelagh Trophy	Notre Dame Vs. Purdue
Silver Spade	New Mexico State Vs. UTEP
Stanford Axe	Cal Vs. Stanford
Sweet Sioux Tomahawk	Illinois Vs. Northwestern
Telephone Trophy	Iowa State Vs. Missouri
Territorial Cup	Arizona Vs. Arizona State
Textile Bowl Trophy	Clemson Vs. NCSU
The Bell	Marshall Vs. Ohio
Tiger Rag	LSU Vs. Tulane
Williams Trophy	Rice Vs. Tulsa