It's not possible to do it faster; according to The Complete Rate-Limiting Guide you
Can only delete own comments under 20 posts per day (multiple comments under same post are treated as one)
This limit applies to both the API and the regular site. Per-app exceptions to the rate limits haven't been made before; the only exceptions I know of are increased daily quota; Smoke Detector has a doubled quota (20,000) and the mobile apps have an essentially unlimited quota.
While cleaning up old comments might be a noble cause, simply deleting them programmatically is not the way to go. It even borders on 'self-destruction of useful content' (a.k.a. 'rage quitting') which is one of the stock reasons to suspend users temporarily. Comments fall under the CC-BY-SA
2.5 3.0 4.0 license too, just like posts.
If you decide to delete old comments, please check whether the content is useful enough to be kept in the post instead. If it doesn't, have a look at other comments under the same post and consider flagging them as 'no longer needed' if they don't make sense anymore (because they were a reply to one of your comments). Flagging as 'no longer needed' doesn't impose any penalties on the user whose comment you're flagging.