Bayonetta Tips

First off: Thanks to the guide at http://scathingaccuracy.com/article.asp?guide/2009.11.08-S.A._Renegade which really helped me (and still does, since I'm not done yet) finding Alfheim Portals and beating them.

While trying, I've found out some things myself that might help peopl beating those events just as they helped me.

Chapter V - Alfheim 10

You gotta stay in the air for 60(!) seconds. The tactics discussed on other sites said to use Shuraba's (the katana) charge attack to stay in the air while using the big head to jump on constantly to stay in the air. But there might be a better/easier way to do this: you need to have Kulshedra (the whip). It has an attack that can pull an enemy from below you towards you (press and hold triangle while in the air). Once you pulled the mob towards you, you can simply jump on it and gain more airtime and simply re-pull him underneath you again.. and so on... that's how I also did the achievement "Higher and Higher". Make sure to only jump once, don't use double-jump since you might need that additional jump in case you run out of enemies to pull underneath you.

Chapter IX - Alfheim 13

Here you have to beat the mobs while being "out of body". Beating them is not hard, but not letting your real self be beat up is annoying. Even at normal difficulty, you always have to watch out.
What I found out though is that if you equip Gaze of Despair, the mobs will all be angered towards you and not even bother about your real body in the bubble. Even when new mobs spawn right next to it, they will be angered right away and also go after you instead.

Chapter XII - Alfheim 18

You got to beat mobs within the time-limit, but they are on fire - well, all except the Manta-rays in wave two. Anyway, you can only hit the mobs with melee during Witch-time. But what helps is that Kulshedra (the whip) can actually hit mobs that are on fire without you taking damage. So use the whip to dish out some damage while you aren't in witch.time. Once you are, switch back to the main dmg-dealing weapon set and do your thing. The whip also works quite well on the Manta rays.