Personal Moveset:
Swords Dance (Breeding w/ Kingler)
Earthquake (TM)
Surf (HM)
Sludge Bomb
First of all, I would like to say that your drawings are very good and pretty cool.
However.
You did not make a good moveset. Let me tell you something: Swords dance and Earthquake on a Water\Poison pokemon is not good. Don't do it.
Here's a much better moveset.(assuming Anenemy can learn them through TM\Move tutor\Breeding.
Surf
Double Team
Toxic
Recover
My reasoning is that Poison is not a strong type. Its only super effective against Grass, and many Grass type pokemon are half poison anyway. As a water\poison pokemon, it's weaknesses skyrocket (as opposed to say, a pure water type, with only two weaknesses)
Those most common added weaknesses include: Psychic and Ground. Both of which are immensly common in competetive play.
Because of Anenemy's vast weakness, stalling moves would be appropriate.
The same thing applies to Tentacruel. Notice that nobody who is serious about the game will ever use Tentacruel for attacking purposes.
Surf isn't a stalling move (obviously) but Anenemy has to be able to attack if say, a ground or rock type pokemon came up.
Double Team obviously for stalling purposes, although don't rely on it for an impervious defense. I once had a Gengar successfully use Hypnosis and two Psychics in a row against my fully double-teamed Ninjask.
Toxic is an excellent move that will KO your opponent if they don't know how to deal with it. The only things you might have to worry about are steel type or other poison-type pokemon. (if you don't know, those types are immune to toxic and all poison moves in general)
Recover is obviously used for regaining HP lost during a battle, though it is a lost cause, as Anenemy will die from one Psychic\Earthquake\Thunderbolt\Solarbeam\Razor Leaf\Confusion\Magnitude\Dig\Thunder\Spark\Volt Tackle\Zap Canon\Psybeam\Bug moves (if playing R\B\Y Stadium 1)\etc..
just to name a few.
Anyway, Anenemy shouldn't really be used for battling anyway, as it will die to pretty much whatever it comes up against. Especially pokemon like Tyraniboah\DD T-tar, Agiligross, Mc IceGar, Espyjump (only for psychic, though), Elemence\DD-mence, McGoose, Curselax, and many others.
Also, your two fossil "pokemon" don't look at all like Pokemon.