LibreOffice doesn't use anything but the freeware font engine so all MS and Monotype fonts will look bad as they are hinted or prepped for the Windows font engine.
Also, LibreOffice doesn't license any fonts from monotype so it's not the best solution if you create a document in Times New Roman in MS office, then open it up in LibreOffice - it will default to some random opensouce (typically poor quality) font.
If the bug is only with a single font:
You can find the fonts in
/usr/share/fonts/truetype and edit them with any application you like.
Remember that in the Ubuntu repository you can find alternative versions of almost any character; often, open versions are better than proprietary ones.
If the bug is with many fonts:
A temporary solution is to use
substitution table in
character styles options to substitute the bad font with the good ones. You can also set the default fonts in the Writer options.
Another solution can be to tweak the characters options for the page: right click -> characters -> position -> distance. And make it fixed by disabling the default, it should be better.
If you can't solve, please consider of downgrading your libreoffice with Synaptics package manager (Menu -> Package -> Force version).
Hope you solve, my eyes would implode with a similar bug. :)
EDIT: if one of the following solutions works try to tweak the font rendering configuration by editing the files in
sudo nano /etc/fonts/conf.d/FILENAME on a terminal to do it.
For example try to disable font antialiasing by editing
10-antialias.conf (replace true with false); the same for
10-hinting.conf. If nothing changes symply re-replace false with true.
Please note that you will disable these features for the whole system, so revert the changes if they doesn't help.
The last possible cause of your problem can be the graphic rendering of the driver itself. You can try to execute
sudo nano /etc/libreoffice/soffice.sh and ENABLE/DISABLE the OpenGL support. Restart Libreoffice after each edit.
If you can't solve downgrade or use OpenOffice or an equivalent suite, for your eyes (I'm not kidding).
I'm sorry if I wasn't of great help, but I don't know the source code of LibreOffice, I'm only trying various possibilities. :-)
Let us know if you solve or if you discover interesting things.
PS: I copied it from Ugly LibreOffice font