Altmetric data in Webometric Analyst is a web site that compiles a range of metrics about academic articles from a range of sources, including Mendeley and Twitter. is similar in this regard to total-Impact, ReaderMeter, ScienceCard, Crowdometer and PaperCritic. The Altmetric Tab gives access to some of these Altmetric statistics. Articles cannot be queried for by name but can be queried for by ArXiv ID, DOI, or PubMed ID.  If you have these IDs for a set of articles, put them in a plain text file, one per line, and click the Get Altmetric Info button.
Alternatively, if you have an API key from you can monitor the site hourly for new information with the Get timeframe results button.