As Slashley mentioned, ult raids vary widely by elements. Also, it's not as simple as getting a certain level of stats. Soul and hime selection makes a huge difference in countering specific boss mechanics (simplest example is you don't bring a debuff team to wind ult.)
If you don't want to get one-shot, technically all you need is hp and heal (well, a lot of ascension with your heals.) Realistically though, it is generally not possible to out-heal ult bosses unless a lot of Andromedas join the raid, so you should be thinking more along the lines of how to deliver maximum dmg before your team starts falling apart. For initial hp level, I would say 10k in-battle is a good starting point to aim for. That allows you to survive most OD so you can react if RNG is being mean to you.
As Slashley mentioned, if there're specific ults you are struggling with, ask away, they're all pretty different.
For AQ5, you don't actually need to survive that nuke to beat it. As long as your two subs can finish off the boss after the main team wipes, it's still victory. This isn't tower or GO where you need everyone surviving. That's how I've been able to AAB AQ5 - my main team wipes about a third to half the time 'cos I'm still weak (and AAB is stupid), but my two subs can finish off the job (actually just one sub is needed - Takeminakata is my answer to most of my problems these days; the other sub is more for insurance.)
If you really want a hard number for reference, I'm currently at ~57k power and recently started being able to AAB AQ5 and all ults except dark (ironic since I main light; also solo-AAB-ing ults isn't 100% success as I rely heavily on debuffs.) No 100% eidolon, but I do have LB3 Hecatonchires (55% char atk and 20% hp) and enough fluffy friends that I can usually get fluffy as support. Importantly though, I own about two-thirds of all the non-limited light SSRs, which gives me A LOT of tactical options.
Listen to Kitty and Slashley and only spend tower medals on bricks please (tickets if you're a gambler.)
The only instance where it might make sense to use medals for HSP is if because of real life constraints you cannot participate in any UE or you're like a stone throw away from unlocking Shingen.