Shrek Forever After was the eighth-highest domestic-grossing film of 2010. Since Shrek Forever After is the fourth movie in the Shrek franchise, I'll first review the original other three Shrek movies. The original Shrek was released in 2001, and was the third-highest domestic-grossing film of its year, behind only Harry Potter and Lord of the Rings.
The first man/ogre to speak is Shrek himself, who reads the fairy tale of Princess Fiona, and then uses the pages of the book as toilet paper.
The men from the village form a mob to kill Shrek. Hiding in the reeds near his house, one of the men wants to charge the house, but two others warn him about what ogres do to humans. Shrek shows up and scares them a bit by talking about what he likes to do to humans (squeezing the jelly out of human eyeballs and using it on toast, for example). One of them waves his torch and says, "Back! Back, beast! I warn you!" Then when Shrek extinguishes the torch by pinching it, the man says, "...Right." Shrek yells at them, and says, "This is the part where you run away." The original Shrek movie passes the Reverse Bechdel test within the first five minutes.
The first woman in the movie is Donkey's owner, who says to him, "Oh, shut up" and slaps him. She only has a few lines before Donkey escapes. When Donkey meets Shrek right after, they have a nice, long conversation that easily passes the Reverse Bechdel. There are some fairy godmothers camped outside Shrek's house, but they don't have any actual lines; they just scream and fly away.
The second woman with lines doesn't show up until about 25 minutes into the movie, during Shrek's wrestling match with Farquaad's champions. A woman in the stands cheers on Shrek and yells to "give him the chair!" which Shrek does by whacking the knight with a folding chair.
Shrek and Donkey have another nice, long, rambling conversation on the way to rescue Fiona. When they get to the castle, Donkey finds out that the dragon is "a girl dragon", but she doesn't have any lines. Fiona herself is the first, and only, woman with more than a single line, about the 36-minute mark.
Throughout the rest of the movie, Fiona only talks to men. There are some background female characters without lines, and of course the speechless dragon, but Shrek never passes the second level of the Original Bechdel test, because there are never two women who talk to each other. According to the IMDB cast list, there were some actresses in the film's choruses, but the only non-chorus actresses listed are for the three female characters that I've already noted above.
Although Shrek fails the Original Bechdel test, it should also be noted that it has very few plot-relevant characters at all. Most of the movie is one-on-one interaction between Donkey and Shrek (who is, after all, the title character). Even so, since the dragon was also female, it would have been easy to give her a few lines, or even add a single scene where Fiona and the dragon talked. After all, both were trapped at that castle for who-knows-how-many years, and yet apparently they never got to know each other.