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Tomato is good at fighting early on due to the lack of many stars lost and the fact that they can revive incredibly quickly.
As Mimyuu, you are focused on using your Hyper as that creates a dynamic with Tomato and generates you even more Hypers.
In lategame, they might falter due to hypers and general power-creep with card levels. In this case, offensive battle cards like I'm on Fire! help seal KOs more safely if it isn't a good time to use Waruda Machine, Blast Off! while defensive cards like Rbits and Rainbow-Colored Circle help against oncoming attacks, especially as Tomato.
Cards that let players draw cards like Nice Present can also create an unsettling Catch-22 with players as they have to risk pulling an Evil Spy Work ― Execution as well as becoming more vulnerable to Tomato if she has a Waruda Machine, Blast Off! in hand. Tomato, however, does not suffer this dilemma due to her passive, which lets her draw cards to her heart's content.
Cards with high star costs/levels or effects that make them difficult to use such as For the Future of the Toy Store and Princess's Privilege can be used to great effect with Tomato's Hyper, as it will make it harder for opponents to empty their hand. Low-norma, low-cost cards that aren't helpful to Tomato & Mimyuu are also a bad idea to deck for this reason.
Scary Solicitation can also be a devastating one if played properly, as it can, at best, make each player lose 45 stars and likely be severely maimed due to potentially pulling multiple copies of Evil Spy Work ― Execution.
Bully characters can consistently keep the duo downed, especially since their ability to act on revival can sometimes mean another catchup opportunity.
Mimyuu loves packing ways to draw cards, but overflowing your hand can let you discard an Evil Spy Work ― Execution before it goes off, wasting 1/4 of the hyper.
This also works against her in the early game, as characters would be more than happy to draw these cards before she can get an Evil Spy Work ― Preparation off.
Characters that do not depend too much on cards such as Star Breaker generally suffer less from both of the duo's hypers as they do not seek out draw panels quite as hard as a character like Arthur would, and thus do not draw Evil Spy Work ― Execution often, or tend to have many cards by the time Tomato approaches them to try and use a Waruda Machine, Blast Off!.
Any source of flat damage such as Long-Distance Shot or Cloud of Seagulls hit the duo much harder than they would anyone else, due to their low max HP.
I'm on Fire! help seal KOs more safely if it isn't a good time to use 
Waruda Machine, Blast Off! while defensive cards like 
Rbits and 
Rainbow-Colored Circle help against oncoming attacks, especially as Tomato.
Nice Present can also create an unsettling Catch-22 with players as they have to risk pulling an 
Evil Spy Work ― Execution as well as becoming more vulnerable to Tomato if she has a 
For the Future of the Toy Store and 
Princess's Privilege can be used to great effect with Tomato's Hyper, as it will make it harder for opponents to empty their hand. Low-norma, low-cost cards that aren't helpful to Tomato & Mimyuu are also a bad idea to deck for this reason.
Scary Solicitation can also be a devastating one if played properly, as it can, at best, make each player lose 45 stars and likely be severely maimed due to potentially pulling multiple copies of 
Passionate Research also automatically pulls 
Nice Jingle can also be of benefit to the duo, as Mimyuu wants to use her hyper the moment she can.
Play of the Gods can pull 
Evil Spy Work ― Preparation if you have it, letting it be played earlier and for cheaper.
Long-Distance Shot or 
Cloud of Seagulls hit the duo much harder than they would anyone else, due to their low max HP.
Shield Counter or 
Reverse Attribute Field
Flamethrower can be used to remove any copies of 
