>>4153542TL;DR plot summary:
the Demon King put a hit on his dad and mom and successfully offed them, also nearly offed Vergil and Dante in the process
Vergil is nonplussed about that and wants to grow stronger to dunk on said Demon King
to do that, he need to raid his crib so that's how 3 happens
since Dante prevents him from visiting the Demon King with full loadout, V gets his shit blasted and becomes a slave to said Demon King, duking it out with Dande till the latter gets said full kit and dunks on the DK (that's 1)
Vergil is mega broken up and salty, so he scours the world to regain Yamato (who since 4 is embedded into the arm of his baby boy, Nero the Deadweight) and have a salty runback with Dante
to have said runback he splits his demon and human halves, and since the demon halves no longer has a human soul to reign it in, it kills couple hundred thousand people to buff itself for said runback (that's how 5 happens)
Nothing in 2 is of any fucking significance