Cut your acrylic on a table saw, that way you can be sure your cutting sqaure and straight.
When you glue only pull back about an inch of paper that is on there for protection.
Tape up your pieces square.
Use a needle applicator with solvent. You can purchase thes at Rockler Woodworking stores for $3.00. It comes out of the bottle fast, but make sure you get enough on to get a good capilary flow into the seam. Only glue horizontal pieces, you will have to adjust and reglue other seams after about 4 hours of set time.
Run a one inch piece of plastic on top for support of your box so that the water doesn't bow it it.
Good luck.