Using the translation table from the Jabref program, finds and replaces all scientific journal names to their standardized abbreviated form. First argument is the file to be processed; outputs safely to 'abbreviated.bib'

Abbreviate Journal Names in Bibtex Database.py

#!/usr/bin/env python
#-*- coding: utf-8 -*-
# Supporting Python 3 

import sys, os, re

try:    bibtexdb = open(sys.argv[1]).read()
except: print("Error: specify the file to be processed!")

if not os.path.isfile('journalList.txt'):
    import urllib
    urllib.urlretrieve("https://raw.githubusercontent.com/JabRef/jabref/master/src/main/resources/journals/journalList.txt", 
            filename="journalList.txt")
rulesfile = open('journalList.txt')

for rule in rulesfile.readlines()[::-1]:           ## reversed alphabetical order matches extended journal names first
    pattern1, pattern2 = rule.strip().split(" = ")
    if pattern1 != pattern1.upper() and (' ' in pattern1):        ## avoid mere abbreviations
        #bibtexdb = bibtexdb.replace(pattern1.strip(), pattern2.strip())    ## problem - this is case sensitive
        repl = re.compile(re.escape(pattern1), re.IGNORECASE)               ## this is more robust, although ca. 10x slower
        (bibtexdb, num_subs) = repl.subn(pattern2, bibtexdb)
        if num_subs > 0:
            print "Replacing '%s' FOR '%s'" % (pattern1, pattern2)

with open('abbreviated.bib', 'w') as outfile:
    outfile.write(bibtexdb)
    print "Bibtex database with abbreviated files saved into 'abbreviated.bib'"

@FilipDominec, feel free to reuse any part of my contribution.

For my own use, I took the code posted by @arahatashun and updated it to pull the latest version of the JabRef lists, which have moved to abbrv.jabref.org and switched to CSV files. It can be found here, in case anyone is interested.