The "Survivor of High Isle" achievement is unlocked when you unlock the in-game achievement of the same name. Getting that one involves unlocking the following other High Isle in-game achievements:
- Champion of High Isle - complete the main story questline
- High Isle Master Explorer - complete the 6 delves and find all the Striking Locales (eye icons)
- High Isle Grand Adventurer - complete 30 unique quests (I believe dailies only count the first time you complete them)
- Defender of High Isle - defeat the 6 world bosses
- Complete the "group event" in the Ghost Haven Bay public dungeon (these are solo-able). The group event is Hadolid Broodmother in the exterior part of the dungeon
- Complete the "group event" in the Spire of the Crimson Coin public dungeon (these are solo-able). The group event is The Crimson Mother in the Prison Warrens part of the dungeon