Lesson 1 - Look for opportunities to play devastating moves, on every move.
Ichigo (talking about Hollow Ichigo): He's spinning Zangetsu around by the wrapping on the hilt! I didn't even know you could do that!
An excellent recent example of this philosophy was on display at Tata Steel chess tournament in Netherlands. Just like Shinji Hirako and Sosuke Aizen, Levon Aronian is a "scary guy".
"I didn't know you could do that!" moves:
19...d5! - Aronian, dude, haven't you read Silman? This move is clearly inferior because you get a bad bishop, duh!
36...Rd8! - Sometimes you have to move backwards to move forwards.
41...Ne1!! - In the words of IM Danny Rensch, "Dude, that move is just SICK!"
Lesson 2 - Always seek out and learn from the strongest opposition.
Ichigo (to Byakuya): Show me your bankai!
For the uninitiated, the chess equivalent would be:
Me (to Kasparov): Show me your 1.e4! Oh, and ... how about loser dies, sound OK?
Lesson 3 - You will get beat, a lot, on the way to greater power.
Ichigo gives it his all, and comes up short vs. Ulquiorra, who stabs him in the chest with his hand. We've all been to Ouchtown.
Lesson 4 - You will fight some battles against real weirdos!
My favorite fellow Mad Scientist, Mayuri Kurotsuchi. You can't play chess for very long before you run into some very odd looking/smelling/acting people.
Lesson 5 - There's nothing wrong with a hard fought draw.
Ichigo and Kenpachi collapse together in a pool of blood. Although it was a draw, few would argue that this wasn't the best fight of the whole Soul Society arc.
Lesson 6 - Above all, chess is a violent game. Make sure you are trying to kill me, cuz I am trying to kill you!
(even when I play the Caro-Kann