When hurting an ender dragon by shooting end crystals, nothing suits the direct_entity "type" condition for the advancement criteria player_hurt_entity.

The Bug

When a player shoots the end crystal that the ender dragon is healing from, nothing you can put for the type of what the direct_entity is will satisfy that condition for the criteria player_hurt_entity.

This is the criteria I was using:

"criteria": {
    "crystactics": {
      "trigger": "minecraft:player_hurt_entity",
      "conditions": {
		"damage": {
			"type": {
				"is_explosion": true,
				"direct_entity": { 
					"type": "minecraft:end_crystal"
				}
			}
		},
        "entity": {
          "type": "minecraft:ender_dragon"
        }
      }
    }

I tried end_crystal, arrow, player and even ender_dragon. Whatever you specify the direct_entity should be, nothing works.

When you punch an end_crystal as opposed to shooting it, "player" will work for direct_entity.

To make things easier, I made a datapack (attached) with all the advancements you need to reproduce the advancement bugs I reported.