I like this guy. It's like a lot of the builds I see at my FLGS: a lot of effort is expended to make the character really good at something. If it's not overwhelmingly powerful, then it's great that the player takes that much interest in builds. If it is, then usually the player has misinterpreted the rule (my favorite being the ranger player who thought the Hunter's Colossus Slayer extra damage went up every turn he kept hitting...)
So, assuming the assassin is 4th level (to get the Crossbow Expert feat) and has set up her shot properly, she makes two attacks at advantage (one attack from the Attack action, the other as a bonus action from Crossbow Expert, at advantage because Assassin). Each one that hits is a critical hit (because Assassin). The hand crossbow damage becomes 2d6 (double the base) + 4d6 (double the Sneak Attack) + Dex bonus (let's assume 4, since to get Crossbow Expert she has forgone getting +2 Dex). The damage range is 11-40 per crossbow, with an average of 25 piercing for the primary attack. The second attack doesn't get Sneak Attack damage, so it only does 6-18 damage, with an average of 11 piercing. Total of 36 average. That's pretty deadly, which is in keeping with the term "assassin."
If the assassin uses poison, that damage also gets doubled. This could be an even more significant bump depending on the poison, although the DMG shies away from making super-deadly poisons easily-available (intentionally).
In the following rounds the Assassin's bonuses go away, and the fact you need to have a hand free to load means only one shot can be taken every round (I'd fight shortsword and crossbow, were it me). This came as a surprise to my players, who expected the Assassin to be a "fighty rogue." My response was, "You want to be the best at fighting, you need to play a Fighter!" This is one of the things I love the most about the new edition.
Anyway, I'll add the following monster/NPC who makes use of this.
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Tz'zird "Tizz" Do'Nerd-on
Medium humanoid (drow), lawful neutral
Armor Class 16 (studded leather)
Hit Points 78 (12d8 + 24)
Speed 30 ft.
STR DEX CON INT WIS CHA
11 (+0) 18 (+4) 14 (+2) 13 (+1) 11 (+0) 11 (+0)
Saves Dex +8, Int +5
Skills Acrobatics +8, Deception +4, Perception +4, Stealth +12
Damage Resistances poison
Senses darkvision 120 ft., passive Perception 14
Languages Elvish, Thieves' Cant, Undercommon
Challenge 8 (3,900 XP)
Assassinate. During her first turn, Tizz has advantage on attack rolls against any creature that hasn't taken a turn. Any hit Tizz scores against a surprised creature is a critical hit.
Crossbow Expert. Being within 5 feet of a hostile creature doesn't impose disadvantage on Tizz's ranged attack rolls.
Evasion. If Tizz is subjected to an effect that allows her to make a Dexterity saving throw to take only half damage, Tizz instead takes no damage if she succeeds on the saving throw, and only half damage if she fails.
Fey Ancestry. Tizz has advantage on saving throws against being charmed, and magic can't put her to sleep.
Innate Spellcasting. Tizz's spellcasting ability is Charisma (spell save DC 10). She can innately cast the following spells, requiring no material components:
At will:
dancing lights
1/day each:
darkness,
faerie fire
Sneak Attack (1/Turn). Tizz deals an extra 13 (4d6) damage when she hits a target with a weapon attack and has advantage on the attack roll, or when the target is within 5 feet of an ally of Tizz's that isn't incapacitated and Tizz doesn't have disadvantage on the attack roll.
Sunlight Sensitivity. While in sunlight, Tizz has disadvantage on attack rolls, as well as on Wisdom (Perception) checks that rely on sight.
ACTIONS
Multiattack. Tizz makes two hand crossbow attacks, or one shortsword attack and one hand crossbow attack.
Shortsword. Melee Weapon Attack: +8 to hit, reach 5 ft., one target.
Hit: 7 (1d6 + 4) piercing damage, and the target must make a DC 15 Constitution saving throw, taking 24 (7d6) poison damage on a failed save, or half as much damage on a successful one.
Hand Crossbow. Ranged Weapon Attack: +8 to hit, range 30/120 ft., one target.
Hit: 7 (1d6 + 4) piercing damage, and the target succeed on a DC 15 Constitution saving throw or be poisoned for 1 hour. If the saving throw fails by 5 or more, the target is also unconscious while poisoned in this way. The target wakes up if it takes damage or if another creature takes an action to shake it awake.
