I don't believe there's a completely legit way to do this.
If you're willing to risk a VAC ban (however unlikely it may be), look at the Steam Achievement Manager. Sketchy-looking site, people use the tool to cheat, use at your own risk, etc. etc. etc. Here are some old Steam forums of people talking about SAM, as well as a previous StackExchange post on the topic. It's against the rules, it's a moral grey area, but for your described purposes, I personally don't see an issue with it.
Otherwise, create a new Steam account, spend $5 on something so you can download all the free games, and start fresh