Use the Regular expression groups:
\[(?<publisher>.*?)\]_Suite_Precure_(?<ep>\d+)_\((?<group>.*?)\)_\[(?<crc>.*?)\].mkv</crc></group></ep></publisher>
This produces 4 groups, so your example becomes:
Publisher CoalGirls
Ep 02
Group 12080x720_Blu-Ray_FLAC
CRC 33D74D55
You can then use these in the Regex.Replace to generate the new name:
${Group}_Suite_Precure_${Ep}_(${Publisher})_[${CRC}].mkv
Produces
1280x720_Blu-Ray_FLAC_Suite_Precure_02_(Coalgirls)_[33D74D55].mkv
However, that is not very user friendly! But it is not easy to do it in a friendly way - you need to specify which "chunks" are which group - which means specifying the start and end sequences, and what to "throw away"
(I had a similar problem when renaming large numbers of files, and ended up writing a GUI interface which helped, but frankly was still a PITA to use.)