You would be able to export “All Assets” from the service desk by clicking on the export option and choosing All Assets from the export dialogue box, like shown in the below image :

However, only the default fields shared across all assets would be available in the export file when you choose ''All Assets''. If you need fields specific to each asset type you would have to choose the particular asset type from the dialogue box like shown in the below image. ( For example : Hardware )

If you would like to have each asset with their fields, we would have to initiate an export for each asset type individually.