From your description, you have a World War II-issue distinctive insigne (DI) of the 135th Infantry. The points (corners) at the top of the shield are squared. The shield is white with a blue St. Andrew's Cross (saltire). A three-leaf clover is in the center. In the white fields, clockwise from the left, there's a figure-eight, a fleur-de-lis (top) and crossed bolos (Filipino knives) on the right. The field at the base of the shield is blank. The regimental motto, "To the Last Man", is embossed on a scroll at the base of the shield.
The regiment was first organized as 1st Minnesota Infantry in 1861 (elements date from 1856). The three-leaf clover was the insigne of the 2d Division, II Army Corps, Army of the Potomac. This and the blue saltire are symbolic of the regiment's Civil War service. The figure-eight, fleur-de-lis and crossed bolos symbolize the regiment's service in the Spanish-Amrican War, World War I and Philippines Campaign, respectively.
The regiment was assigned to 34th Infantry Division from 1917 to 1946, then assigned to 47th Infantry Division, Minnesota National Guard, in June 1946. The DI or crest issued subsequent to the regiment's re-assignment differs in that the shield has three points at the top and the sides are rounded, joining at a single point at the base. The symbolism is the same except that a bull's skull was added in the white field at the base of the shield. Adapted from the insigne of the 34th Infantry Division, this commemorates the regiment's twenty-nine years as an organic element of the division.