Checkpoints are found throughout Gamer 2. If Hailey dies during the game, she'll respawn at the furthest checkpoint she's reached in the level. Checkpoints with deflector plates inside them will also reactivate Hailey's deflector plate if she's currently missing it. Hailey's progress will not be lost if she respawns; enemies will remain dead and map objectives (such as collecting the derezzer or destroying the fence with the airstrike) will remain completed.
There are two checkpoints each in the rooftops level and streets level, and one each in the menu level, building level and factory level. The checkpoint in the arena level is visibly broken and Hailey's progress will not be saved if she dies; she'll be forced to restart the boss fight from the beginning. The falling level has no checkpoints and must also be restarted upon death.