Tetris Attack was fun to be crappy at back in the old days. I say the old days since now I'm a champion Tetris Attack player, so I'm no longer crappy at it.
As for the second boss, just keep moving left and right. He's actually pretty easy. There's a Homing Missile power up in this stage, try not to lose it, and save it for the boss fight. Point the Homing Missile up, but keep your eye on the bottom screen. Most of his attacks involve the tail, and occasionally grab the entire bridge.
His second form is even easier. Just shoot him!