The acoustic scattering properties of nondiffracting high-order Bessel trigonometric beams (HOBTBs) by fluid spheres are investigated. The three-dimensional directivity acoustic scattering patterns of hexane, red blood, and mercury soft spheres immersed in water and centered on the beam axis of wave propagation are presented and discussed. HOBTBs belong to the family of nondiffracting beams and are proper solutions of the homogeneous (source-free) Helmholtz equation. Closed-form analytical solutions for the incident and scattered pressure fields are provided. The far-field acoustic scattering field is expressed as a partial wave series involving the scattering angle relative to the beam axis, the order, and the half-conical angle of the wave number components of the HOBTB. The properties of the acoustic scattering by fluid spheres are discussed and numerical computations with animated graphics show exciting scattering phenomena that are especially useful in applications related to particle entrapment and manipulation of soft matter using acoustic HOBTBs. Other potential applications may include medical or nondestructive ultrasound imaging with contrast agents, or monitoring of the manufacturing processes of sample soft matter systems with HOBTBs.