Hello,
Please disable the plugin "HikaSerials - HikaShop Integration plugin" in your Joomla backend.
Then, perform a new test in your checkout.
Regarding the error message, we have not information on which "elements" is using too much memory, but the issue occurs in the Log System, not in HikaShop or HikaSerial.
Nevertheless, increasing the memory limitation in your hosting could be a good solution.
Specially if you are trying to generate big images with the "attach serial" plugin ; that kind of processing need to load the entire image (uncompressed) in memory in order to modify it with the rest of the content.
Regards,
Jerome - Obsidev.com
HikaMarket & HikaSerial developer / HikaShop core dev team.
Also helping the HikaShop support team when having some time or couldn't sleep.
By the way, do not send me private message, use the "contact us" form instead.