The API does not provide a good way for this.
Worst case, your app will have to keep a table of every question in the tags of interest. Poll that table and see if the accept status has changed from the last stored answer id, if any.
Beware that, depending on what tags you search, and how often you poll, your app may bust its quota.
If you don't mind data that's up to a week old, you can use the Data Explorer (SEDE) to get answers by tag and by accept date.
See this query of Answers that were accepted after a given date and for given tags.
If/Once you know the question IDs, you can use the /questions/{ids}/timeline
route to determine the exact time an answer was accepted.
For example, your sample question shows the following times in the API:
"timeline_type": "question" => creation_date = 1442856640 (2015-09-21 17:30:40 UTC)
"timeline_type": "answer" => creation_date = 1442903871 (2015-09-22 06:37:51 UTC)
"timeline_type": "accepted_answer" => creation_date = 1442943688 (2015-09-22 17:41:28 UTC)
Note that neither your sample question, nor its answer, have been edited. If they had, then "timeline_type": "revision"
event(s) would have appeared as well.
Also, /questions/{ids}/timeline
has a fromdate
parameter, which theoretically would help you. However, this is still broken.
Go upvote the bug report in the hopes that it attracts some developer love.
Finally, if you can make a case for searching by accept date, you can go to Meta Stack Exchange and make a feature request. Once it's on the main sites, then we might be able to use it via the /search
paths or get it added to the API.