Seagull best played as an opportunist rather than a bully. Even the meekest characters are capable of deadly retaliation if they survive due to Seagull's bad defense, evasion, and health pool.
Johnathan Rush reduces the victim's defense by 1. Use this to your advantage, especially when in a desperate situation.
Jonathan Rush combos extremely well with any offensive battle card, such as Big Magnum or even Accel Hyper.
Cards that cause multiple battle phases, like Little War, may backfire, as giving an opponent the ability to counter attack multiple times will usually result in death.
If planning on using expensive battle cards to secure kills, President's Privilege may be worth while. It greatly reduces their cost and allows for Johnathan Rush to be played in the same turn for much cheaper.
Dash! is a double edged sword. It does allow Seagull to catch up to weak enemies, but also allows other players like to catch up to Seagull. Offensive characters like Yuki can take advantage of this to score easy wins off of Seagull.