  Representative samples of F-, G-, K-type stars located out of the Solar
Neighbourhood has started to be available in spectroscopic surveys. The
fraction of metal-poor ([Fe/H]~$\lesssim -0.8$~dex) giants becomes increasingly
relevant to far distances. In metal-poor stars, effective temperatures
($T_{\mathrm{eff}}$) based on LTE spectroscopy and on former
colour-$T_{\mathrm{eff}}$ relations of still wide use have been reported to be
inaccurate. It is necessary to re-calibrate chemical abundances based on these
$T_{\mathrm{eff}}$ scales in the multiple available surveys to bring them to
the same standard scale for their simultaneous use. For that, a complete sample
of standards is required, which so far, is restricted to a few stars with
quasi-direct $T_{\mathrm{eff}}$ measurements. We aim at providing a legacy
sample of metal-poor standards with proven accurate atmospheric parameters. We
add 47 giants to the sample of metal-poor dwarfs of Giribaldi et al. 2021,
thereby constituting the Titans metal-poor reference stars. $T_{\mathrm{eff}}$
was derived by 3D non-LTE H$\alpha$ modelling, whose accuracy was tested
against interferometry and InfraRed Flux Method (IRFM). Surface gravity (log
$g$) was derived by fitting Mg~I~b triplet lines, whose accuracy was tested
against asteroseismology. Metallicity was derived using Fe II lines, which was
verified to be identical to the [Fe/H] derived from non-LTE spectral synthesis.
$T_{\mathrm{eff}}$ from 3D non-LTE H$\alpha$ is equivalent to interferometric
and IRFM temperatures within a $\pm$46~K uncertainty. We achieved precision of
$\sim$50~K for 34 stars with spectra with the highest S/N. For log $g$, we
achieved a total uncertainty of $\pm$0.15~dex. For [Fe/H], we obtained a total
uncertainty of $\pm$0.09~dex. We find that the ionization equilibrium of Fe
lines under LTE is not valid in metal-poor giants.
