Femtosecond nonlinear optical imaging with nanoscale spatial resolution would provide access to coupled degrees of freedom and ultrafast response functions on the characteristic length scales of electronic and vibrational excitations. Although near-field microscopy provides the desired spatial resolution, the design of a broadband high-contrast nanoprobe for ultrafast temporal resolution is challenging due to the inherently weak nonlinear optical signals generated in subwavelength volumes. Here, we demonstrate broadband four-wave mixing with enhanced nonlinear frequency conversion efficiency at the apex of a nanometre conical tip. Far-field light is coupled through a grating at the shaft of the tip, generating plasmons that propagate to the apex while undergoing asymptotic compression and amplification, resulting in a nonlinear conversion efficiency of up to 1 x 10(-5). We apply this nonlinear nanoprobe to image the few-femtosecond coherent dynamics of plasmonic hotspots on a nanostructured gold surface with spatial resolution of a few tens of nanometres. The approach can be generalized towards spatiotemporal imaging and control of coherent dynamics on the nanoscale, including the extension to multidimensional spectroscopy and imaging.