Cosmogenic radio-nuclei are an important source of background for low-energy neutrino experiments. In Borexino, cosmogenic $^{11}$C decays outnumber solar $pep$ and CNO neutrino events by about ten to one. Highly efficient identification of this background is mandatory for these neutrino analyses. We present here the details of the most consolidated strategy, used throughout Borexino solar neutrino measurements. It hinges upon finding the space-time correlations between $^{11}$C decays, the preceding parent muons and the accompanying neutrons. This article describes the working principles and evaluates the performance of this Three-Fold Coincidence (TFC) technique in its two current implementations: a hard-cut and a likelihood-based approach. Both show stable performances throughout Borexino Phases II (2012-2016) and III (2016-2020) data sets, with a $^{11}$C tagging efficiency of $sim$90 % and $sim$63-66 % of the exposure surviving the tagging. We present also a novel technique that targets specifically $^{11}$C produced in high-multiplicity during major spallation events. Such $^{11}$C appear as a burst of events, whose space-time correlation can be exploited. Burst identification can be combined with the TFC to obtain about the same tagging efficiency of $sim$90 % but with a higher fraction of the exposure surviving, in the range of $sim$66-68 %.
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