This game provides examples of the following tropes:
Action Girl: Both Detective Carrie and Jill; the latter punched out the final boss with her own fist! Oh, there is others besides those two, The Magnet Sisters count and perhaps the most overlooked of them all, Jill's Mother.
Arson, Murder, and Jaywalking: When Jill gets taken away by a police trap, as the police chief reads her crimes, they were of breaking in the Skullker HQ, robbing of the Art Museum, defiling the ruins where the Blue Diamond is, causing havoc at Metal City, and 17 counts of skipping restaurant bills.
Arguably a Scrappy Mechanic as well, since the only other use for the chips is to buy upgrades. You have to pay for Continues.
It's not so bad, as with all the upgrades you'll make way more than 50 chips before you're even CLOSE to dying. Hard mode requires 10 but this is burned away quickly by bosses unless you start over every time you die.
No Export for You: in Europe, unsurprisingly. Fellow bigger-cartridge game WarioWare Twisted shared the same fate.
No-Gear Level / Stealth-Based Mission: The opening of Area 5-1. Jill is imprisoned and separated from the Dozer, which is powered by a diamond until it finds her.
Punched Across the Room: Certain Skullker robots, most notably the ones in the fifth secret area.
Also the final boss.
The Power of Love: When Jill is captured by a police trap, and separated from her Drill Dozer, it pilots itself back to her, through the power of her deceased mother's spirit.
Recurring Boss: Detective Carrie's Policebot, and Croog.
Tennis Boss: The upgraded Policebot in Area 4-1. Combat revolves around catching the explosive projectile with your drill and sending it back — but this is complicated by having to identify whether to catch it clockwise or counterclockwise (otherwise it explodes and damages you), and the ten-second countdown attached to it as you deflect the projectile back and forth between player and boss.
Speaking of Lagann, a lot of people think that Drill Dozer was inspired by that show because they are so similar (mainly because of the characters and the use of robots and drills). The truth is, the game came out first (2005), Gurren came out after (2007).
Timed Mission: Occurs during mission 6-1, when you have to stop the gigantic Drill Missile from destroying your home base (where Dad is recovering).
Also the fifth boss.
Tube Travel: The many threaded tunnels that require drilling one way or the other to enter and navigate. Defeating the boss of Area 5 involved being able to navigate tunnels within a time limit to destroy the boss's weak points.
Turns Red: Most of the Humongous Mecha bosses get more aggressive after part of them is destroyed.
Also, the robot dog enemies turn white after you do some damage to them.