This does the trick:
use 5.010;
use DateTime::Format::ISO8601;
say DateTime::Format::ISO8601
-> parse_datetime('2012-02-25T18:48:34.835-05:00')
-> strftime('%F %T');
However, note that you're dropping the time zone altogether! Unless you know that all the Atom entries have been posted from the same time zone, this is a bad idea.
An entry dated 2012-02-25T12:00:00+12:00 was written a full day earlier than one at 2012-02-25T12:00:00-12:00, yet using the conversion above, they'd both get formatted as 2012-02-25 12:00:00.
To solve that you could normalise them all to the same time zone before formatting. UTC is the time zone most commonly used for that purpose.
use 5.010;
use DateTime::Format::ISO8601;
say DateTime::Format::ISO8601
-> parse_datetime('2012-02-25T18:48:34.835-05:00')
-> set_time_zone('UTC')
-> strftime('%F %T');