Since this is one of the numerous achievements that take place exclusively in the Spaceship, the biggest concern would be the prerequisites needed to be satisfied before the area or object could be accessed. Since Rumbi is in the main room of the Spaceship, this is not an issue and makes the achievement possible to accomplish without even entering Welcome to Mafia Town.
Since the action of attempting the achievement is the only limiting factor to its completion, being able to predict and land on top of a moving target like Rumbi will be the only source of difficulty in this achievement.
Prediction of where Rumbi will be as Hat Kid lands from a jump is a good intuition to utilize, given the moderate speed it can build up once it is uninhibited by knockback and wide turning can lead to several missed jumps. It is important to know however that Rumbi is tall enough to require at least a single jump from the same level of floor to get on top it's hitbox.
Attacking Rumbi with the Umbrella or even bare-handed can be beneficial to riding it, as the knockback animation allows for a short time frame where it stays on the floor and able to be ridden upon but does not move. This can also occur when it drives into a wall. Mind however that attacking Rumbi bare-handed will result in Hat Kid jumping thrice in pain, leaving enough room for Rumbi to escape its stun lock. To prevent escape, moving during one of the jumps to stand in front of Rumbi will cause it to be stunned again, with enough time to ride it.
As mentioned, any contact with a solid object will leave Rumbi stunned for a period of time, but will also turn its direction of movement 180 degrees to face the opposite direction of the obstetrical it collided with. This has the potential benefit of the player wedging Rumbi between themselves and a wall, effectively stun locking it until the player moves out of the way.
Inversely, it does a complete 360 degree turn from where damage is dealt, making attacks unfeasible to manipulating where Rumbi will move towards with attacks alone given where they land on the target highly varies where it will travel. It does however have the benefit of moving Rumbi backwards from where it is hit, making it better for pushing into more susceptible locations that body blocking couldn't accomplish.
If all else fails, waiting while Rumbi cleans can lead to a mall window where Rumbi does a short animation of twirling, bounding in place or harshly moving over a select area. All of these have the same effect as a normal stun, allowing the player to approach Rumbi and ride it.