The plot is contrived, cliched, and only semi-coherent. All the 1960s stereotypes are here, including the young artist struggling to find himself, the girl who loses her boyfriend in Vietnam and goes on to become an anti-war activist, the guy who gets sent to Vietnam and (naturally) goes crazy, etc. None of the characters are especially likable.
Clearly this movie was made with the sole intent of mashing together a bunch of Beatles music videos. If you really, really love the Beatles and their music, then you'd probably get a kick out of this cheesy little project, but if you're only a casual fan, you're not likely to be impressed.
Basically, "Across the Universe" is to the Beatles what "Mamma Mia!" is to ABBA. If that doesn't sound appealing to you, then skip this one.