I have faced this issues couple times on different Ubuntu versions while trying to install MariaDB (fully compatible MySQL replacement DB)
dpkg: error processing /var/cache/apt/archives/libmysqlclient18_5.5.33a+maria-1~raring_amd64.deb (--unpack): libmysqlclient18:amd64 5.5.33a+maria-1~raring (Multi-Arch: no) is not co-installable with libmysqlclient18 which has multiple installed instances
as I understand "old" version of libmysqlclient18 is already installed and for some reason system can't resolve what to do with current lib as some other soft depends on it.
search for a line with
and remove block of text till lines
this text block could appear couple times there, remove all appearances.
after that run
apt-get -f install
Such "hack" helped with some other libs also, whenyou are sure that you have installed correct version of library or you have a PPA with needed version, but
apt-get does not see it. Try do the same manual cache clean for this lib.