The phrase "bear up against" can be replaced with a variety of synonyms depending on the context of the sentence. If you mean to withstand or endure a challenge, you could use words like persevere, weather, survive, or endure. If you mean to confront or face a difficult situation, you could use words like confront, face, tackle, or combat. To handle or cope with heavy emotional or physical strain, you could use words like sustain, maintain, or soldier on. All of these synonyms carry slightly different nuances, so it's important to choose the one that best fits the tone and context of your writing.