Cid acquires Dynamite after using his default Limit, Boost Jump, 7 times. A quick way to fill his Limit gauge is to inflict him with Fury, and equip him with Cover. Fighting enemies that deal fractional damage is also a good way to raise the Limit gauge; the forest in Nibel Area after Mt. Nibel is an especially good Limit grinding spot for its Battery Caps and Valrons. The area is already available by the time Cid joins the party.
Cid lights a stick of dynamite with his cigarette, then hurls it at the enemy party, doing 21⁄4 times normal damage to all enemies. It is superior to his starter Limit Break, Boost Jump, against groups of enemies as it targets all opposition, but against single enemies, such as most bosses, Hyper Jump remains the better option as it deals more damage. Dynamite is eclipsed by his Level 2 Hyper Jump, learned after Cid kills 60 enemies.