It's done pretty well so far, but I'd still apreciate your opinion.
Pokemon (22)
2xLapras fossil
2xPsyduck fossil
2xPsyduck team rocket
4xGolduck fossil
4xArticuno fossil
4xMr. Mime jungle
4xMewtwo movie promo# 3
Trainers (10)
2xPlus Power
2xProf. Oak
2xEnergy Removal
3xSuper Energy Removal
Energy (28) 
17xWater Energy
11xPsychic Energy
The only vulnerability I could think of is a stall deck (I have one of those too...), and I haven't come against anyone using rocket or gym cards.  I would just appreciate a DCI or casual fix to kill the weaknesses.

Okay - we'll go for a nice little casual fix here.  IMHO, that's the first step.

Immediately I notice something - 10 trainers.  Not NEARLY enough.  So, we have to cut elsewhere.  Let's see where to go first....

Pokemon numbers are too high.  Let's cut a good number of them.

First of all, get rid of the Lapras's all together.  Nice thought, but not needed.  Take out a Golduck - only need about 3 here.  Take all the Fossil Articunos, and make them 2 Movie Promo Articunos - they deal a little less damage, but retreat for less, and can do bench damage for one less energy, which combos well with Mime.  Speaking of the Psychic bad-boys, drop down to 2 Mimes and 3 Mewtwos.

Energy is also WAY too high.  We can afford to drop the Psychic by about 3 down to 8, and the Water by 6, down to 11.

After the smokes clears, we have freed 17 slots for trainers.  This is real good because we needed them.

We're going to start by adding in a 3rd Oak and 4 Bills.  Card drawing is good!  Seeing as though we have a solid Energy Removal theme going here, let's add in 2 more Energy Removals.  Computer Search and Item Finder are our friends, so let's add in 3 of each to find and re-use what we need.  Scoop-Up is very versatile, and good to have 2 of in the deck.  2 Nightly Garbage Run will round out the initial trainers.  I'm not overly fond of the Gamblers and the PlusPowers, so we're going to pull them.  Needing a Gym in case No Removal shows up, let's use the Rocket Training Gym.  This helps keeps Pokemon secure as we're holding them in place, beating on them.  Two of those are good.  With the last slot, go for Gust of Wind.  I'm not a big fan of only 1 Gust in a deck, but I like the idea of 1 Gust rather than none.  Here is the final product:

2 Psyduck (Rocket)
2 Psyduck (Fossil)
3 Golduck (Fossil)
2 Articuno (Movie Promo)
2 Mr. Mime
3 Mewtwo (Movie Promo)

8 Psychic Energy
11 Water Energy

3 Professor Oak
4 Energy Removal
3 Super Energy Removal
4 Bill
3 Computer Search
3 Item Finder
2 Scoop Up
2 Nightly Garbage Run
2 The Rocket's Training Gym
1 Gust of Wind

Give it a try and hopefully you'll like it a little better.  Have a great day!