We present X-ray images of Tycho's supernova remnant in emission-line features of Mg, Si, S, Ar, Ca, and Fe, plus the continuum, using data obtained by the imaging spectrometers on board the Advanced Satellite for Cosmology and Astrophysics (ASCA). All the images show the shell-like morphology characteristic of previously obtained broadband X-ray images, but they are clearly distinct from each other. We use image reconstruction techniques to achieve a spatial resolution of ~08. Line intensity ratios are used to make inferences about the remnant's physical state, on average for the entire remnant and with angular position around the rim. The average temperature of the Si and S ejecta in the remnant is (0.8-1.1) × 107 K, and the average ionization age is (0.8-1.3) × 1011 cm-3 s. For a constant ionization age, the observed relative brightness variations of Si and S line image profiles with azimuthal angle imply differences of roughly a factor of 1.3-1.8 in the temperature. We compare the radial brightness profiles of our images with simple geometrical models and find that a spherical emitting geometry is favored over a torus. A spherical geometry is further supported by the absence of systematic Doppler shifts across the remnant. The radial fit results also suggest that some radial mixing of the ejecta has occurred. However, the azimuthally averaged Fe K image peaks at a markedly lower radius than the other images. The average Fe K/Fe L line intensity ratio and the position of the Fe K energy centroid support a temperature several times higher and an ionization age approximately a factor of 10 lower than for the other elements, and imply that the Fe ejecta must have retained some of its stratification. Although many of the features in the 4-6 keV X-ray continuum correspond to those in the radio, there is no obvious correlation between the relative brightness in these bands.