Titanic Ant can use PSI Magnet. This means that you will probably run out of PP before the end of the battle. For that reason, bring food with you into battle.

Titanic Ant is flanked by a couple of Black Antoids. They can use PSI Lifeup to heal the Titanic Ant. However, they can only do so for about five turns, after which they'll run out of PP.

Titanic Ant can cast Shield α, which will reduce the effectiveness of your physical attacks.

Since you will likely run out of PSI anyway, use PSI Rockin α on the first turn if you have it. This way, you get rid of the Black Antoids in one blow so you won't have to worry about their Lifeup spells anymore. However, PSI Rockin is expensive, and you might want to conserve your PP for healing.

The lowest level that Ness can be and still have a chance to defeat Titanic Ant is 5. It will be very difficult, but not impossible at this level.