Kathy has pretty much said it all. What I suggest you do in addition is re-read the instructions on the DIF. The KEY points are: 1) Wearing gloves and using boiling, hot water. Always work with VERY hot water; NOT warm water. 2) You need to make sure your Paper Tiger is not 'plugged up' and free of debris. Check it periodically. This is important because the key, here, is to be sure the Tiger is completely PERFORATING the paper. If it's not, then the DIF won't get to the glue! 3) You need to wait the 15 minutes, and do a 2nd coat and wait a 2nd 15 minutes. What you do is apply the DIF to an area of about 10' x 8'. Then wait 15 minutes. Re-apply and do a 2ND wall, and wait 15 minutes. After that 2nd 15 minutes, re-apply to the 2nd wall (which is its 2nd coating), and go back and start removing the paper on the 1st wall (which already had its 2nd DIF coating.) This way, you can kinda start working on a wall (that's been coated 2x's), while a 2nd wall's DIF solution is 'working'. If necessary, do a 3rd coating but don't wait the 15 minutes - Go right at it (while the wall is really wet.)
I recommend using a sponge that's used to wash a car. One of those BIG, bulky sponges. If you have a lot to do, you can consider a garden sprayer. (It's a LOT easier on your back!) Lay plastic on the floor, and then lay a sheet or 2 of newspaper on TOP of the plastic to soak up the water. If you have baseboard trim running along the bottom of your walls, keep them clean by wiping them often. You DON'T want the glue residue / wet wallpaper drying on it. (It's a bit of a pain to remove ...)
And lastly, if you have vinyl wallpaper, or vinyl-coated wallpaper, the job won't be easy. IF your efforts actually remove the vinyl BUT leave some paper (and glue) behind, that's OK. Just go about applying the DIR solution to what's left on the wall, and wait 15 minutes. Since in this case it's only paper and glue, you may not need a 2nd coat. If you do, just re-wet it and don't wait the 2nd 15 minutes. A 3" spackeling knife is good for doing this job.
If you have more ?'s, e-mail me directly or post up. My best to you and hope this helps.