Are you sure it’s your y-axis? Your x-axis belt tension seems way too loose. The belt shouldn’t be able to swing around like that.
You could try this: Ultimate Wanhao i3 Plus Belt tensioner by coreygeorge - Thingiverse 29
It’s hard to tell the issue with just the video. What upgrades have you done, what slicer, what print settings, is that a stock build plate, are those stock bearings on the y-axis?
It seems like the y-axis is getting caught on something, check and make sure there’s nothing getting caught on the y-axis. Does the bed move freely by hand? Is the pulley for the belt getting stuck?
It’s probably an issue with the crappy lm8luu bearings on the printer, and you might have to replace them.