To obtain this achievement you'll first need to be playing as Salvador and have reached level 5, as Gunzerking is his unique Action Skill. Now that you're playing as him, there's a few Skills you're going to have to buy from your Skill Trees before you can stay in Gunzerking mode for 90 second, so this will take some levelling to reach them.

Below are the Skills you'll have to purchase;

Rampage Skill Tree

Last Longer: Makes gunzerking last longer.

Yippie Ki Yay: Increases the duration of dual-wielding every time an enemy is killed while Gunzerking.

Now that you have them, you're good to go for 90 seconds. All you need now is enough enemies to keep it going. I got it in the bandit slaughter dome. This is easier to get playing solo because then you don't have to worry about other people stealing much need kills.

Remember to use strong guns.