Dear Ayushi Garg

You can get any DEM data ASTER and SRTM from the two websites below

1- https://earthexplorer.usgs.gov/

2- http://gdex.cr.usgs.gov/gdex/

The two websites need registration 

Regard

https://earthexplorer.usgs.gov/

http://gdex.cr.usgs.gov/gdex/

on earth explorer you can find DTM data free

See if you can find something useful through NASA's Earthdata Search database. They have a good collection of data from earlier research that they have made publicly available. Try changing the browse collection via the Subsetting Services. Check attached link for an example. Also refer to the webinar link. 

https://search.earthdata.nasa.gov/search?m=-16.661194499999993!161.68260987499997!5!1!0!0%2C2&q=DEM&ok=DEM+Vanuatu&sb=166.524979%2C-20.248945%2C170.234772%2C-13.073444&fst0=Land+Surface&fsm0=Topography&fs10=Terrain+Elevation&fs20=Digital+Elevation%2FTerrain+Model+(Dem)

https://www.youtube.com/watch?v=5Ssh1lu3InI

Hi James, Thanks for your reply. could you please tell me more about this, like, how to refine this search.

Thanks to all for your valuable answers. I'm waiting for some more suggestions as my project demands that there should be no SRTM data. and the ASTER data i have found is not of good quality.

You might want to do a search of the literature to locate researchers that may have collected topographic survey for their Vanuatu projects and contact them directly to request access to their data.

Please try,

 www.hydrosheds.org/page/availability

The new JAXA ALOS World 3D is 30m resolution and freely available from OpenTopography here: http://opentopo.sdsc.edu/raster?opentopoID=OTALOS.112016.4326.2