Crown of the Ivory King

The Crown of the Ivory King doesn't boost your stats, but it restores your HP at a rate of 2 HP every 3 seconds.

Frozen Eleum Loyce

Location of Garrison Ward Key, Dark Souls 2: SotFS

Collect the Garrison Ward Key, which opens the door to the Expulsion Chamber bonfire. The nearby stone coffin transports you to the Frigid Outskirt, the gauntlet area of the DLC. There are no notable loots at the Frigid Outskirt and defeating the gank boss there wouldn't yield anything useful (apart from the boss souls). It's OK to skip the Frigid Outskirt. Next, rescue Loyce Knight x 3, who will help you during the fight against the Burnt Ivory King. Collect the Ring of Resistance+1, useful for boosting your petrify defense by 200 points. Equip the ring when dashing through areas where enemies can build up your petrify metre. Locate a room that holds five iron chests, one of which is a Mimic. One of the chests contains a Titanite Slab and another chest contains Brightbug x 2.

Brightbug x 2 and Titanite Slab at Frozen Eleum Loyce, Dark Souls 2: SotFS

Burnt Ivory King

SL1 Burnt Ivory King, Dark Souls 2: SotFS

This boss is weak against lightning. Buff your Raw Ice Rapier+10 with Gold Pine Resin. The Ice Rapier is recommended for two reasons. First, unlike the Rapier, the Ice Rapier can build up the bleed bar of the Burnt Ivory King, or any enemy that is vulnerable to bleed. Second, the Ice Rapier has a faster attack animation than the Mace or Homunculus Mace. You will have many opportunities to output two hits with the Ice Rapier. However, note that the Raw Rapier+10 deals more damage than the Raw Ice Rapier+10 and it's very likely that you will never bleed the boss at all during the whole fight.

Defeat the Burnt Ivory King and collect the Crown of the Ivory King.