If anyone who's watched SpongeBob recalls the episode "MermaidPants", you might remember that it's heavily implied Squidward (as Doctor Negative) was trying to get SpongeBob and Patrick killed by frying them to death.
This isn't the only episode where Squidward intentionally caused harm to the two (or at least one of them) as in several (in particular, recent) episodes he's seen trying to get them hurt in one way or another--take "Sportz?" for example. He manipulated SpongeBob and Patrick into hurting each other by using sports gear the wrong way. We can also very clearly see that this is in fact causing them injury and pain. And this was all intentional.
There's also been plenty of other cases where he tried to manipulate the duo into getting themselves hurt, such as in "The Curse of Bikini Bottom" where he allowed SpongeBob and Patrick to play with his lawn mower, clearly expecting them to get hurt or possibly killed. In "Life Insurance", he also tried manipulating the two into hurting each other, believing they genuinely would since they thought their contracts made them invincible. In "Broken Alarm", he even seems excited at the thought of SpongeBob having died or gotten seriously hurt.
Squidward's hatred of SpongeBob and Patrick is understandable due to them constantly putting him through a lot of trouble, but he often does some things to them that are very illegal. Often times he would take it too far, and while he did feel bad about it in the first few seasons, he seemingly shedded this quality later on. I'd argue it's enough to qualify him as an actual villain, but what do you think?