You get the option to purchase the Laser Pet at Level 20. You must buy all the upgrades and the pet to get the achievement, but you do not need to purchase the Level Up option for pets.
Purchase Rocket Pet - $3000
Upgrade 1 - $5000
Upgrade 2 - $7000
Final Upgrade - $9000
TOTAL COST - $24000
(edit costs thanks to SwankyCriminal)
STRATEGY: I personally went for this by saving up all my money from the first 20 levels. You get the checkpoint after defeating the second boss, and should have around $20000 at that point going into Level 21. You can then finish Level 21 and buy the Rocket pet to the max and quit out. You will then be reset to the start of Level 21 with all your money back (and will have that checkpoint saved for future use). If you do not have enough money, simply save more to be able to buy the Rocket pet to max after a level in one go.
Another great strategy point is to leave the powerups on the stage and shoot through them. As your bullets move through the powerups, they will take on the characteristic of the powerup. This is especially great for drones placed next to the powerups. Note that the invulnerability, smart bombs, and shield upgrade do not let bullets pass through.