Tonberry uses Traveler every turn, doing Defense-ignoring damage to a party member. They counter every attack with their special attack. Knife, doing heavy physical damage, followed by Traveler. This combo is powerful and will likely kill any party member it hits unless they are at a very high level. The Tonberry is vulnerable to the Imp spell, which will prevent it from using Traveler, but it will always get a critical hit with its normal attacks while imp. It is also susceptible to Petrify. The Break spell will fail because Tonberries are immune to Death, but Gau's DeepeyeRage works well, as its Dread Gaze attack (which inflicts Petrify) does not check for Death protection like Break does.
A way to win against Tonberry with low-level characters is to take one with 255 Defense and put him/her in the back row with a Ribbon or Jeweled Ring. The main problem with Tonberry is that it will use Traveler when hit or killed, and the player might not be able to withstand the attack unless they have high HP from the Muscle Belt and/or Red Cap.
If the player cannot get their HP higher than Traveler's damage, they will have to ensure it can't be used, as there is no reliable method of healing. The only way to do that is to drain Tonberry's massive pool of MP, which will take hundreds of turns. The most reliable chance of avoiding a counterattack is for the player to wait until it uses all of its MP via Break spells (which the player should be protected against), while holding and to have the character try to run away so they won't attack Tonberry prematurely and trigger a counterattack.
If the character is strong enough to survive a single Traveler strike, an effective strategy is equipping the Master's Scroll and Black Belt. Since the Tonberry has a 66% chance of opening with either Attack or Knife, this gives the character a good probability of killing the Tonberry immediately by counterattacking and following with a normal attack.