Hey,
I do this on a daily basis. Your workflow in ArcGIS will depend on what format the bathymetry data is in. For instance, is it a Raster (.ASC), Netcdf, .XYZ, etc...
You'll goal is to create a raster, or import the already created raster that was delivered to you. From the raster, you'll be able to identify slopes, depths, produce hillshades and whatever else you may need to do..