W4R-D3N can be tricky if you're solo'ing the game and aren't playing one of the classes that has a "bullet sponge" as an action skill. There are a few things you can do to make this easier, though.
First, since this is playthrough 1 and you've got lots of easy levels to gain, you might consider grinding a few levels. Your damage output is somewhat affected by the level difference between you and an enemy, so you'll likely find it much easier to take him down if you're a few levels higher. If you've skipped any side missions, now is a good time, or you could fight back through the Ramparts a time or two.
Second, you might want to consider rapid fire weapons for this fight. There's not a lot of room to maneuver, and there's a lot of things vying for your attention. Don't get me wrong - it's certainly possible to do this with a sniper, but you might have an easier time with something you can quickly fire an entire clip from and then dodge afterwards.
Also, possessing a corrosive and/or slag weapon goes a long way. Loaders and Constructors are common enemies from here on out, and they go down so much easier with a good corrosive weapon. Grinding, gambling, shopping, and opening the golden key chest are all good things to do to find some better/different weapons.
When W4R-D3N calls for backup and badass loaders spawn, put something between you and the boss, and focus on these loaders instead. At least take down the badasses before you return your attention to the boss directly. You can use the cover strategically to keep a large percentage of the enemies from targeting you at once.
Finally, the weaker loaders can be de-fanged by shooting their arms and/or legs off. Then you can leave them around to give you a quick way to get back up should W4R-D3N down you during the fight.