- Build a recovery environment. Rebuild the server from backup. Use Microsoft's ExMerge tool to extract messages of interest (you'd have to confirm whether ExMerge will let you find the messages with attachments based on some criteria that defines "important") into .PST files. Then use ExMerge to import those into your production server. Test in a lab first.
- Find a third-party utility that let's you do item-level recovery from regular backups. Search for "Exchange recovery item-level" using your favorite search engine. That would save on having to build the recovery environment and would give you more criteria to choose from in extracting messages and attachments from the backup.
Unfortunately there is no other easier way.
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