Death attack is an assassin ability.
At 1st level, the assassin can make a special sneak attack called a Death Attack. This functions exactly like rogue's sneak attack ability, except that the attack has a chance of paralyzing the target. The assassin's Death Attack inflicts an extra 1d6 points of damage. This bonus rises to +2d6 at 3rd level, +3d6 at 5th level, +4d6 at 7th level and +5d6 at 9th level.
Death attack does not normally work against creatures immune to critical hits. However, if the assassin has Epic Precision, then death attack will bypass such immunity entirely, dealing full damage but does not paralyze the target. This is contrary to the in-game description of the feat.
The DC for the paralysis attempt is 10+(Assassin Class Level)+(Intelligence Modifier). So a level 8 Assassin with an intelligence of 20 would have a DC of 23.
This ability has a powerful interaction with Manyshot. Every time two arrows are notched instead of one, both arrows will deal death attack damage and potentially paralyze the target. As such, a character with 7 or more ranged attacks per round (3 in the first "flurry") using manyshot on an unsuspecting opponent will deal six death attacks, causing high damage and forcing six fortitude saves, paralyzing the target if at least one save fails.