Poison Ivy has never pulled any punches with Batman, and things are no different for her appearance in "Arkham Asylum." By the time you find her hiding within the plant-infested hallways, she's gathered enough power that she can completely shield herself for much of the fight; you can't just use brute force to power your way through this battle.
Use the Line Launcher in the Botanical Gardens to pass over the Flooded Corridor. Previously, one of Poison Ivy's tendrils was blocking the path, but you can access her lair after finding the Batcave during the story. A cutscene plays upon entering the lair.
Roll out of the way frequently to dodge Ivy's plants; she has a few vines sticking out to start, but she'll summon more to rise from the ground; they'll cause moderate damage if they connect.
Fire your Batarang at her shield, poking for light damage while Ivy herself is protected. Be careful not to throw too many times between dodges; without any upgrades, you shouldn't toss the Batarang more than once before dodging the vines.
Strike Ivy with the Batarang when the shield pops open. The first time, you shouldn't have much trouble, and she'll scream when struck.
Dodge the energy balls she begins firing in your direction. Now you'll need to keep striking Ivy until she reveals herself again; this time you must keep dodging vines and the new projectiles. Striking Ivy directly a second time may take a couple of tries.
Strike at Ivy once more to end the fight. This will be the most difficult because she begins firing the energy balls at a faster rate, creating dangerous lines as long as her own vines. Hitting her directly the final time may take several tries; as long as you keep dodging and throwing persistently, you'll eventually make it without succumbing to her damage.
Having the Quick Batarang upgrade makes this fight much easier.
Although you might want to attack Ivy as rapidly as possible, err on the side of caution; running the risk of getting caught in those vines and taking damage isn't worth getting another shot off. As is often the case, Batman's best assets here are patience and determination, not firepower.