I think these are not good enough answer(s)... many involve a couple of extra under-the-hood steps. Here's how I did it.
sudo apt-get install jq
...because the JSON output needs to be consumed after you call the API.
#!/bin/bash
server_addr = 'jenkins'
server_port = '8080'
curl -s -k "http://${server_addr}:${server_port}/pluginManager/api/json?depth=1" \
| jq '.plugins[]|{shortName, version,longName,url}' -c | sort \
> plugin-list
echo "dude, here's your list: "
cat plugin-list