I will assume that you are allowed to crack the .zips you will be cracking.
We will use fcrackzip for this. I could not get the much more known John The Ripper to work reliably in this case.
wget http://oldhome.schmorp.de/marc/data/fcrackzip-1.0.tar.gz
tar xf fcrackzip-1.0.tar.gz
cd fcrackzip-1.0
./configure
make
sudo make install
Suppose we know that the password ist a five digit PIN consisting only of numbers, padded with zeros. We create a wordlist of all possible passwords:
typeset -Z5 i ; for i in {0..99999} ; do echo $i ; done > /tmp/wordlist
Then we use that wordlist with fcrackzip:
/usr/local/bin/fcrackzip --use-unzip --dictionary -p /tmp/wordlist ~/my-zip-file.zip