Hi there. I believe there are 15 levels in the Eager Beaver game. I was surprised when I got to the end and got my trophy so I am not 100% positive. I think I was expecting at least 20 levels and wasn't paying close attention when the fanfare and congratulations began. I will say that it was the easiest trophy for me to get - I got it on my 4th time playing. I have tried to win other trophies and have had to play games sooooo many times and only have 4 trophies so far. I think it really helped that I could take my time in the Eager Beaver game and come up with some long words. Good luck to you!
First I was hoping for 10 levels, then after 11 or 12 I expected 20, and dreaded 30.
But it turns out ther are 15 levels. 15 very long and strenuous levels.