Hey, I was looking into this as I recently purchased a PSP and I came across this article which explains Elite Squadron is the best PSP Battlefront to date.
"...While Elite Squadron is undoubtedly the best PSP Battlefront yet, loving it unreservedly relies more on your love of Star Wars than its sometimes frustrating mechanics. Nevertheless, this is still epic, cracking Star Wars battling..."
http://www.gamesradar.com/psp/star-wars-battlefront-elite-squadron/review/star-wars-battlefront-elite-squadron/a-20091103101125523071/g-2009052610344642064
EDIT: Also, yes, Elite Squadron has single player modes.