This was a walkthrough on how to beat the Road Trip. Solutions are subject to change if Plants vs. Zombies Adventures is updated. Please report in the comments if a solution to a level doesn't work for you.
Use Wall-nuts on every level (except for level 1 since it starts with 2) and use about 3 or 4 Aspearagus, as well as 3 Sunflowers and some Peashooters.
Since you can only use 4 plants, You can't use all plants. Ditch out Peashooter for Cherry Bomb. Use Cherry Bomb when there are a lot of zombies. Other than that, do the same as Dire Spries.
The 5th pot is a must. Buy it before playing any levels. Use Beet on the fifth pot. Put Beets next to Wall-nuts for a good offense. Other than that, do the same as other levels.
Use Snow Pea instead of Aspearagus this time. Put Snow Pea closer to the paths and zombies they can kill them. Other then that, Do the same as other levels.
Use Jalapenos on levels with a lot of crossroads. other than that, do the same as other levels.
U of Z
The 6th Pot is a must. Buy it before playing any level. Use Magnet Plants when a Football Zombie comes. Use only 2 of them. Other than that, do the same as any other level.
Never try to enter a level without a decent amount of Flaming Peas, due to the big amount of Ice Block Zombies. Depending on the level layout, use either Cherry Bombs or Jalapenos as the instant kill.
It is recommended to bring Shamrocks to every level, since now the first zombie of a level is always a Conehead Zombie. The Imposter Zombie is a tough zombie, so it is recommended to use strong firepower on it, and freeze it frequently. Due to the amount of zombies that can eat Wall-nuts easier(Football Zombies, Ice Block Zombies and Imposter Zombies), using the Beet and the Wall-nut together becomes difficult. Cherry Bombs and Jalapeños are good to blast away conga lines, Imposter Zombies, and any other major threats.
Grey Matter Gardens
Keep using Shamrocks as your first shooting plants, as Conehead Zombies and Buckethead Zombies do not stop being the first zombies. Bamboo Shoots take a long time to harvest and cost 800 coins to harvest, so smart usage of them is recommended. Bamboo Shoot is stronger and has longer range than Beet, so it is preferred to use Bamboo Shoot to them. Mall Cop Zombies are very resistant, as even Bamboo Shoots and Shamrocks have a hard time taking them down without ZombiFreeze. On later levels, instant kills become closer to needed.
The Sever Glades
Repeaters are a fairly useful plant to use. They are less expensive(as they cost only 100 sun) than Shamrocks and can deal with Bucketheads without ZombiFreeze occasionally. They harvest quicker than Shamrock and Bamboo Shoot, so Repeaters are definitely a usable plant, though technically they aren't necessary. Magnet Plants can be used against Weightlifter Zombies, but Repeaters, Bamboo Shoots, and/or Shamrocks with ZombiFreeze will probably do. When things start getting rough, instant kills can give an easier clearing.
The Sand Dooms
Snow Pea is a lot more relevant during The Sand Dooms, due to the appearance of Gas Can Zombies. Gas Can Zombies aren't threats whenever you have Snow Peas, and are occasional threats when you don't. The stronger threats come from tough zombie combinations and sometimes unfavorable layouts. Instant kills are not necessary, though they come closer to that later on. Repeater, Bamboo Shoot and Shamrock still remain as the powerful plants, their usage remaining the same as in earlier maps.
Only 2 or 3 Twin Sunflowers max are needed per level, so spend more time and sun on your other plants. It is recommended to bring Snow Pea to every level with Gas Can Zombies and/or Rocket Zombies, as they are potential threats. Gargantuar Zombies are variably defeatable, though for the most part it relies on freezing them while they are being taken care of by your powerful plants, and sometimes using instant kills to take a chunk of their health away. Depending on the level layout, Repeater or Shamrock may be the more favorable first shooting plant.