In "The Moebius Factor," Kerrigan will walk across a pre-destined path through the map, stopping to investigate empty buildings. The player must destroy the data cores before Kerrigan reaches one, or the mission is lost. Kerrigan cannot be killed and attacks the player if approached, so it is best to avoid her.
In "All In," Kerrigan will periodically attack the player's base. She can quickly demolish defensive structures and units, and will use her Implosion ability to instantly destroy mechanical units. When killed, she returns to her base to recover and attacks again some time later. On hard/brutal, in addition to having increased health and energy, Kerrigan will also be accompanied by Hunter Killers.
In addition to her normal abilities, Kerrigan has a hidden damage barrier, similar to the immortal's Hardened Shields, that reduces all incoming damage from attacks to 6, and also reduces the damage taken from spells. For this reason, it is best to assail her with a large force of marines. The science vessel's Irradiate also helps to whittle her HP down quickly.