If an opponent would gain life, that player loses that much life instead.
If more than one replacement effect tries to apply to a life gain event, the player who would gain life chooses the order in which they apply. For example, if a player who controls Alhammarret’s Archive would gain 3 life while Tainted Remedy is on the battlefield, that player may choose to have the 3 life become doubled to 6 life and then lose 6 life. The player may also choose to apply Tainted Remedy first, turning “gain 3 life” into “lose 3 life.” Alhammarret’s Archive would then not apply.
Having more than one Tainted Remedy on the battlefield doesn’t have any noticeable effect on life gain. Once the effect of one Tainted Remedy applies, there is no life gain for the others to apply to.