(Tips, not an exhaustive guide.)
First, some links with in-depth descriptions of what is generally considered traits of anti-heroes.
Basically, an anti-hero is someone who does heroic things usually using unheroic means or for unheroic reasons.
Why isn’t your character a hero?
>What would a true hero do if they were placed in the situation that your character is in?
>What, of those things, would your character never do?
Why is your character not a villain?
>What have they done that assures no one would label them villain?
Why is your character not a civilian?
>What has your character done that has set them apart from completely non-heroic civilians?
What are your character’s flaws?
>Is there anything about your character’s appearance that is distinctly unheroic?
>>Do they look frightening?
>>Are they objectively ugly?
>>Do they dress in an unusual or inappropriate manner?
>Is there anything about their personality that doesn’t mesh with the “hero” mold?
>>Are they rude?
>>Are they anti-social?
>>Do they complain a lot?
>>Do they make inappropriate jokes?
>>Are they anti-authority even when the authorities are respectable?
>>Do they have a dislike for, or prejudice against, a group of people (mainly concerning immutable traits)?
>>Are they immature?
>>Do they swear frequently?
>Is your character’s alignment generally unsuitable for heroic endeavors?
>>Is your character more “neutral” than “good”?
>>Does your character completely disregard the laws of the setting?
>>Does your character think activities that others may consider heinous to be morally okay?
>>Does your character just happen to be the lesser of two evils?
>Is your character’s motive selfish or otherwise unheroic?
>>Are their motives for doing good more selfish than altruistic?
>>Do they only do these things for attention?
>>Are they completing an act of personal revenge that happens to align with public interests?
>>Do they think that doing a heroic thing will make it easier for them to find a significant other?
>>Are they only doing heroic things because they flipped a coin and decided to go with it?
>>Are they doing it because they’re bored?
>>Because they’re being paid?
What are your character’s positive (traditionally heroic) traits?
>When a battle breaks out, will they try to warn civilians to stay away?
>Are they brave in the face of danger?
>Would they still help or save people they don’t like?
>Do they have a day job that makes them an “everyday hero” like firefighting or the like?
>Do they have an unwavering moral code (regardless of whether the code in question is particularly heroic or not)?
Remember to create a balance between the two, otherwise you may end up with a slightly-less-than-ideal hero, or a villain with a good trait or two (also known as a well-developed villain).