Also I need help with Baal Avatar, and yes, I did read the wiki.
Don't bother raising your affinities for this fight, as he's only got 1 elemental spell, and it's really weak anyway. Silence is the only status effect you need to guard against. With that in mind, use your equipment slots to either raise the defense/HP of your more durable characters, or just focus on offense. The latter half of the fight will be a damage race.
You need 2 strong tanks for this fight. Meiling or Tenshi should occupy the first slot, while the 2nd slot should go to whoever you have with great DEF and HP, like Yuugi, Wriggle, or Remilia. Ideally, you have at least 2 characters for the 2nd slot. Group healing with Reimu will be extremely important (although you can get away with MAG-buffed Rumia). Group DEF buffs are also crucial, so Reimu, Yukari, Ran, and Keine are all in high demand. The job of your 2nd slot character shouldn't be to deal damage, since they will be taking heavy damage from row-based attacks and can rarely afford to have their action bar low. Let them assist the tank in switching out slots 2 and 3. One of those slots should be rotating strong attackers (Kanako is great here for double damage on Suiga), while the other should be using Reimu for healing and your buffer of choice for DEF (use an attacker if buffs are full and healing isn't needed).
Alternatively, if you have several attackers with reasonable survivability but not to the level of Yuugi or so, you can switch out slot 2 with your tank while being careful not to have a weakened character out when the boss attacks. This works best with Tenshi, who requires less healing anyway. You can then have more semi-permament members in slots 3 or 4.
Play defensively for the first half of the fight and prioritize buffs and healing over damage. If you have Iku, let her take slot 3 or 4 for a while and have her buff your attackers as they're coming in (but don't be afraid to switch her out if you need defensive buffs or healing). Ran can also work in offensive buffs into her routine if you're using her. Count your damage carefully. After you've dealt 3 million damage (not 4 million, like the wiki says), the Baal Avatar will start gaining a significant amount of ATK and SPD every single turn. At this point, your goal is to merely give him as few remaining turns as possible. If you've been using Iku or Ran, you should ideally have several buffed attackers at this point. Otherwise, you can switch Rinnosuke into slot 1 and let him buff 3 characters quickly (he'll die soon, so switch in your tank once that happens). If your slot 2 character is also a good attacker like Yuugi, then you can try to blitz the boss with Yukari's Spiriting Away and at least 2 attackers. Otherwise, start switching in attackers into both slots 3 and 4, using Reimu for group healing when needed and switching in DEF buffs less frequently. Even though you're damage racing at this point, you still want Tenshi or Meiling in slot 1.