SmashManiac: Never heard of this game, but judging by the comments, it looks very interesting.
However it seems that the story is tightly linked to the 1st game which I never played and it also seems to be an important part of the experience, so I'm going to hold off for now.
By the way, what's up with the death by cow screenshot? O_o
My wife (who played the series before marrying me) actually played this game before playing the first one and said she didn't feel like she had missed anything.
They do have an optional "here's what happened in the first game" bit during a fake newscast in the game if you want to see it, but honestly, these are the only things a person ought to know about the first game before playing this one:
*You're a time travel agent
*You saved the world in the last game and everyone thinks you're a hero
That's it. The hows or whys don't matter all that much because they aren't relevant to the story in this one. (And, in fact, the main character is the only one who is brought back from the first game.)
The death-by-cow screenshot is actually one of the funnier gags in the game. You're trying to scale a castle wall in a medieval time period and the defenders are chucking boulders at you. If you wait and stand still too long, they fling the cow, bringing an unfortunate (if not hilarious) end to your time traveling career.