Found this wiki entry. Copying the following line into your /etc/default/grub will do the trick:
GRUB_CMDLINE_LINUX_DEFAULT="quiet loglevel=3 rd.systemd.show_status=auto rd.udev.log-priority=3 loglevel=0"
This is likely to appear in line 9, and you won't need to type again
GRUB_CMDLINE_LINUX_DEFAULT=. Note that
vga=current didn't work for me, and although the wiki recommended it, it converted my bootsplash into an ugly gray screen with three dots, try it anyway in case it solved your problem.
Next, it is really important to add
loglevel=<level>, where, citing the wiki,
is any number between 0 and 7, where 0 is the most critical, and 7 is debug levels of printing.
This is what really solved my problem, as my screen didn't stop displaying level 3 and lower alerts. Changing it to 0 is the way to go if you don't want to be bothered unless your computer is in a real trouble... don't worry, you'll be notified instantly if any error makes your machine catch fire.