CYBERTAXONOMY: Apparently coined by Quentin Wheeler in 2002. Malte Ebach and others suggested four possible definitions a few years later, and Ebach distilled these into "an integrated way to do taxonomy using standardized electronic tools and resources" in 2007 (https://cybertaxonomy.eu/blog/2007/04/11/what-is-cybertaxonomy.html).
HYPERTAXONOMY: First used in 1989 to describe a HyperCard method to store herbarium taxonomy data (https://www.jstor.org/stable/1222633?seq=1#page_scan_tab_contents). The word appears in the 2018 Decadal Plan as shorthand for "the comprehensive documentation of Australian and New Zealand species before mid-century".
TURBOTAXONOMY: Possibly first used in 2012 to describe a study of braconid wasps "based largely on COI barcoded specimens, with rapid descriptions of 179 new species" (http://www.mapress.com/zootaxa/list/2012/3457.html).
PRAGMATICOTAXONOMY: From the Greek "pragmaticos", proposed here to describe what taxonomists do, without hype.