Played the single player campaign on Normal difficulty, switching to Hard now. What should I be doing differently, even the first intro scenario is kicking my tail. Do I avoid unessential targets/fights and just go for the stated goal? Hard is so much more difficult than normal.... Advice, suggestions, etc. are welcome, please!
You need to be familiar with micro and macromanagement, hotkeys, and fundamental game mechanics like high ground advantage, field of view. You need to know counters more and generally you need to multitask more.
The only hard part in the first scenario is attacking at the exact same time as your reinforcements that come down in drop pods. If you can get that right, the rest is easy. As for the rest, I suggest you actually practice in quick matches or against AI. You need good base management and unit control to get through most hard missions. Things like having enough workers, having enough barracks, factories, starports (and constantly training units from them) etc.
Right on, try hard AI in custom games, they will get your skills up to par as far as base management and macros.