Void Walker
+9 to Blood Claws damage = 15 unholy, 90% accuracy
Precision of the Assassin ignores soaks
First hit: Enervation + 15 unholy
Second hit: 16 unholy (Rend Flesh)
Third hit: 17 unholy (Rend Flesh)

-------- THE SCENARIO IN WHICH THERE IS LESS HELP --------

(1000 Alcohol Drunk:
Bar base find 20% chance (indoors)
+ 10% for building light = 30%
+ 10% from Search = 40%
+ 15% from Opal Syndicate = 55%
Alcohol find chance (based off weight table) 82.2% * 55% = 45.21% chance per AP
To find all the alcohol = 1000/0.4521 = 2212 AP
Total AP spent = 2212 AP + 1000 AP (to ruin your liver) + 20 for guild = 3232 AP
> HC Cloak of Water +10% to base = 65%
> 82.2% * 65% = 53.43% chance per AP
> To find all the alcohol 1000/0.5343 = 1872 AP
> 1872/70 = 27 AP cycles
> 1872 + 27 = 1899 => +1000 AP to drink +20 for guild = 2919 AP

1000 Food Eaten:
Bakery base find 30% chance (indoors)
+ 35% for light, Search, Opal Syndicate = 65%
Food find chance (no Butterscotch Pie :() 96.49% * 65% = 62.72% chance per AP
To find all the food = 1000/0.6272 = 1595 AP (rounded up) + 1000 to eat = 2595 AP
> HC Cloak of Water = 96.49% * 75% = 72.37% chance per AP
> To find all the food 1000/0.7237 = 1382 AP
> 1382/70 = 20 AP cycles
> 1382 + 20 = 1402 => +1000 AP to eat = 2402 AP

AP spent on Alcohol and Food: 3232 + 2595 = 5827 AP
> AP spent on Alcohol and Food for HC: 5321 AP)

BUT

1000 Food Eaten:
Restaurant base find 30%? chance (indoors)
+35% for light, Search, Opal Syndicate = 65%
Food find chance 62.5% * 65% = 40.625% chance per AP
(Alcohol find chance 29.69% * 65% = 19.3% chance per AP)
To find all the food = 1000/0.40625 = 2462 AP + 1000 to eat = 3462 AP
(Alcohol found along the way = 2462 * 19.3% = 475)
> HC Cloak of Water = 62.5% * 75% = 46.875% chance per AP
> To find all the food = 1000/0.46875 = 2134 AP
> 2134/70 = 31 AP cycles
> 2134 + 31 = 2165 => +1000 AP to eat = 3165 AP

1000 Alcohol Drunk:
Bar base find 20% chance (indoors)
+35% for light, Search, Opal Syndicate = 55%
Alcohol find chance (based off weight table) 82.2% * 55% = 45.21% chance per AP
To find all the alcohol = (1000-475)/0.4521 = 1162 AP
Total AP spent = 1162 AP + 1000 AP (to ruin your liver) + 20 for guild = 2182 AP
> HC Cloak of Water +10% to base = 65%
> 82.2% * 65% = 53.43% chance per AP
> To find all the alcohol (1000-475)/0.5343 = 983 AP
> 983/70 = 15 AP cycles
> 983 + 15 = 998 => +1000 AP to drink +20 for guild = 2018 AP

AP spent on Alcohol and Food: 3462 + 2182 = 5644 AP
> AP spent on Alcohol and Food: 3165 + 2018 = 5183 AP

1000 Books Read:
Library base find 30% chance (indoors)
+ 35% for light, Search, Opal Syndicate = 65%
Book find chance 63.48% * 65% = 41.262% chance per AP
To find all the books = 1000/0.41262 = 2424 AP (rounded up) + 1000 to read = 3424 AP
> HC Cloak of Water = 63.48% * 75% = 47.61% chance per AP
> To find all the books 1000/0.4761 = 2101 AP
> 2101/70 = 31 AP cycles
> 2101 + 31 = 2132 => +1000 AP to read = 3132 AP

1000 Deaths: 1 AP per respawn at level 1 = 1000 AP

1000 Doors Destroyed/1000 Doors Repaired:
Assuming you destroy a door that's just one repair step away from destruction (15 hp):
1 hit to destroy a door = 1000 AP
5 AP to repair a door = 5000 AP
Assuming you miss the door when trying to destroy it 10% of the time,
1000/0.9 = 1112 AP
6112 AP

1000 Pills Taken:
Pharmacy base find 30% chance (indoors)
+ 35% for light, Search, Opal Syndicate = 65%
Pills find chance 50% * 65% = 32.5% chance per AP
(FAKs find chance 41.67% * 65% = 27.09% chance per AP)
To find all the pills = 1000/0.325 = 3077 AP + 1000 to eat = 4077 AP
(FAKs found along the way = 3077 * 27.09% = 833)
> HC Cloak of Water = 50% * 75% = 37.5% chance per AP
> To find all the pills 1000/0.375 = 2667 AP
> (FAKs find chance 41.67% * 75% = 31.25% chance per AP)
> 2667/70 = 39 AP cycles
> 2667 + 39 = 2706 => +1000 AP to eat = 3706 AP
> (FAKs found along the way = 2706 * 31.25% = 846)

20000 HP Healed:
1 AP to heal 15 + 10 HP (FAKs, Surgery, Knot of Keepers) = 25 HP
Don't need FAKs; found them all while searching for pills \o/
800 to heal + 20 for guild = 820 AP

1000 Items Crafted:
Crafting carving knives with Wondercraft = 12-6 = 6 AP per knife (destroyed) = 6000 + 20 = 6020 AP
Finding chunks of steel in a factory = 22.06% * 65% = 14.34% chance per AP
To find all the steel = 1000/0.1434 = 6974 AP
6974 + 6020 = 12994 AP

1000 Items Repaired:
5-3 = 2 AP per repair = 2000 AP

1000 Locks Picked:
60% chance of success for having lockpicks and the Lockpicking skill
1000 AP/0.6 = 1667 AP

1000 Power Removed/1000 Power Restored:
Assuming you're teaming up with a helpful person,
5 AP per building to remove power; 5 AP per building to restore power = 5000 + 5000 = 10000 AP

1000 Targets Shot:
2212 AP to find bottles in a bar
128 AP for travel
338 AP to find quivers
Assuming you're missing 5% of the time with a compound bow,
1000/0.95 = 1053 AP and shots
Reload 1053/10 = 106 times => 1053+106 = 1159 AP
Total = 2212 + 128 + 338 + 1159 = 3837 AP

1000 Angels Killed:
If all the angels killed are shepherds,
Three hits + Enervation + 1 use of Hellfire = 3 AP, 15 MP
Assuming four hits after MP runs out,
(3 AP * 3 kills) = 9 AP; (71 AP - 9 AP)/4 hits = 15 (rounded down) kills
15 + 9 = 24 kills per 71 AP cycle
1000/24 kills = 42 (rounded up) AP cycles = 42*71 = 2982 AP
90% hit chance, so assume 10% are misses = 2982/0.9 = 3313 AP
Assuming 5% are critical hits, and therefore 1 fewer AP is needed to kill that target = 3313 AP - 0.05(3313) = 3148 AP

1000 Demons Killed: See Angels Killed = 3148 AP

1000 Kills:
0 AP; you've already gotten this badge from killing all those angels and demons, you monster.

100000 Damage Dealt:
Assuming each target has 50 to 60 HP and they were at full health,
2000 kills already (demons and angels) = all the damage dealt needed already, so 0 AP

100000 Damage Taken:
If you have 71 hp, then the deaths badge will already have given you
71000 damage taken

1000 Pets Killed:
Killing imps or aethersprites = 1 hit + 1 use of Hellfire = 1 AP, 10 MP
Assuming 2 hits after MP runs out,
(1 AP * 4 kills) = 4 AP; (71 AP - 4 AP)/2 hits = 33 (rounded down) kills
33 + 4 = 37 kills per 71 AP cycle
1000/37 = 28 (rounded up) AP cycles = 1988 AP
Assuming 10% are misses = 1988/0.9 = 2208 AP
Assuming 5% are crits, which means 1 fewer AP = 2208 - 0.05*2208 = 2098 AP

VW End AP: 59677 = 622 days = 1.7 years
Too tired to calculate HC damage, but if it doesn't lag too far behind the VW, then HC should still come out with fewer AP spent.