business competition purposefully attack the competition

The practice of showing the competitions product, likeness, or information inside your advertising is called comparative advertising.

There really isn't an ad term for slandering the competition beyond legal terms like slander and defamation. There are an abundance of laws on the books to keep this kind of thing from happening.

Not saying this doesn't happen but this is usually in small markets/towns. Some of the words around these ads are attacks and battles.

The term negative advertising is most often used for political ads, but is also used occasionally for non-political marketing that directly attacks a competitor.

The term more commonly used in an advertising context, as RyeBread suggests, is comparative advertising. This is a more neutral term and includes more neutral comparisons ("The same towels at a lower price") that might not be considered an "attack" or "slander."

Terms such as trade libel or defamation are legal terms. Not all comparative advertising, or even all negative advertising, is illegal, so these have a much narrower sense.