Well welcome to the club if you are having trouble. For all the car's nice features, the convertible top mechanism on the Allante is highly problematic, especially in the early models like yours. There's even a separate booklet on *just* erecting and collapsing the convertible top.
I found you an owner's manual on eBay. it's pricey but I think you'll find it more than worth it.
1988 Allante Owner's Manual
If you can't get the back cover open, then you probably have a stretched cable or busted latch---also a known issue.