Although it depends what your research essay is on (i.e. you can't use the same idioms if you are writing an essay on a novel character and on a historical event), there are a few good ones that can be used to show off your knowledge of Spanish in the majority of essays:
1. Ver las orejas al lobo - To see the danger signs (Really good also for cultural / contemporary ones in the discursive essay, or when discussing a character's relationship with another character.)
2. Al fin y al cabo - Finally / At the end of the day / When all is said and done (Good for conclusions.)
3. Valer la pena - To be worth it / To be worthwhile
4. Tener en mente - To keep in mind (Good for comparisons, or when transitioning from advantages to disadvantages. E.g. "Sin embargo, necesitamos tener en mente que...")
5. Ir de mal en peor - To go from bad to worse (You can use this when talking about a character's progression, or even about a negative event in history. It's rather versatile.)
These idiomatic phrases are particularly good as they are not that informal, and at least one can be used in every single essay!