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Use Mega Drain first, to restore some health. Next, use Grass Knot if it is currently outside the water, and try to trap it. If it is in the water, use Body Slam to knock it out instead. Either way, use Mega Drain to finish.
Mega Drain->Grass Knot if Staryu outside water, attempt trap->Mega Drain ->Body Slam if Staryu in water, knock it onto land->
With both Pokemon preparing for full out offense and not too much health each, it looks like this will be the last round. Patrick starts with an Ice Beam at Treewig, and Treewig responds with a Mega Drain to try to stay alive a bit longer. Patrick shoots an Aurora Beam at Treewig, who uses a Knot of Grass to trip Patrick. It looks like both Pokemon are within one hit of being KOed! Patrick is faster and simply shoots a Beam of Ice Treewig, finishing this match.
Patrick the Staryu
HP: 15
Energy: 63
Atk: 1
Def: 2
SpA: 4
SpD: 2
Spe: 85
Stuff: none
On a side note, I think that my inexperience probably cost me the match. I used a lot of things that were only questionably useful (status at the beginning LOL). Also, if Destiny Bond had KOed Monohm...